{"id":307648,"date":"2022-11-08T20:39:00","date_gmt":"2022-11-08T13:39:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=307648"},"modified":"2023-02-06T10:18:18","modified_gmt":"2023-02-06T03:18:18","slug":"contoh-soal-relasi-dan-fungsi","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/contoh-soal-relasi-dan-fungsi\/","title":{"rendered":"Kumpulan Contoh Soal Relasi dan Fungsi Lengkap dengan Jawaban dan Pembahasan"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1280\" height=\"853\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-cottonbro-studio-5184943.webp\" alt=\"\" class=\"wp-image-307664\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-cottonbro-studio-5184943.webp 1280w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-cottonbro-studio-5184943-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-cottonbro-studio-5184943-1200x800.webp 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-cottonbro-studio-5184943-1170x780.webp 1170w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-cottonbro-studio-5184943-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-cottonbro-studio-5184943-263x175.webp?crop=1 263w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, apakah kamu gemar bermain <em>puzzle<\/em>? Tentu kamu tahu bahwa setiap kepingan <em>puzzle<\/em> hanya bisa mengisi satu bentuk posisi dan tidak bisa digantikan oleh kepingan yang lain. Di dalam Matematika, kondisi semacam ini disebut sebagai fungsi.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Di artikel sebelumnya, Quipperian sudah pernah belajar tentang <a href=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/relasi-dan-fungsi\/\">pengertian relasi dan fungsi<\/a>, perbedaan antara relasi dan fungsi, serta cara menyatakan keduanya. Di artikel ini, Quipperian akan diajak untuk melihat beberapa contoh soal terkait dengan relasi dan fungsi. Yuk, simak selengkapnya!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 1<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Perhatikan koordinat Cartesius berikut ini.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/u_28-4nxthhsfEMoGSKM8YgP4lr2UTiwMZjcmY4LAYVrlT9FXRc-AHQvPkpclYpZWrif0afkYu_7QWI82JZQCSWJWDQ1FbhhULbKTLH-dVm_8PT1g0hLHVspZZIfWkbtVY7l4x2j4Mzkf-DgLiZaF1j8YWhEiUUebH0M_Pd5ZA3pJ4HnU7R8EGTBMsRgqQthO_lEpr9Ftw\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Himpunan yang sesuai dengan relasi di atas adalah \u2026.<\/p>\n\n\n\n<ol type=\"A\">\n\t<li style=\"list-style:upper-latin;\">{(Febri, bakso), (Ani, soto), (Johan, bakso), (Gilang, rawon)}<\/li>\n\t<li style=\"list-style:upper-latin;\">{(Febri, Johan, bakso), (Ani, soto), (Gilang, rawon)}<\/li>\n\t<li style=\"list-style:upper-latin;\">{(Bakso, Febri), (Soto, Ani), (Bakso, Johan), (Rawon, Gilang)}<\/li>\n\t<li style=\"list-style:upper-latin;\">{(Bakso, Febri, Johan), (Soto, Ani), (Rawon, Gilang)}<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dari diagram Cartesius pada soal, diketahui bahwa sumbu-x (A) merupakan nama orang dan sumbu-y (B) merupakan nama makanan yang disukai oleh orang yang namanya ada di sumbu-x. Dengan demikian, relasi antara A dan B adalah sebagai berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Febri menyukai bakso.<\/li>\n\n\n\n<li>Ani menyukai soto.<\/li>\n\n\n\n<li>Johan menyukai bakso.<\/li>\n\n\n\n<li>Gilang menyukai rawon.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Jika dinyatakan dalam bentuk himpunan menjadi seperti berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">{(Febri, bakso), (Ani, soto), (Johan, bakso), (Gilang, rawon)}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Penulisan himpunan di atas tidak bisa dibalik, ya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, himpunan yang sesuai dengan relasi di atas adalah {(Febri, bakso), (Ani, soto), (Johan, bakso), (Gilang, rawon)}.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: A<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 2<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui <em>f<\/em> merupakan fungsi himpunan P = {1, 2, 3} ke himpunan Q = {5, 11, 21}. Jika dinyatakan secara berpasangan menjadi <em>f<\/em>: A \ud83e\udc6a B = {(1, 5), (2, 11), (3, 21)}. Rumus fungsi <em>f<\/em> adalah \u2026.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n\n\n\n<li><\/li>\n\n\n\n<li><em>f<\/em>(<em>x<\/em>) = 2<em>x<\/em><sup>2<\/sup> + 1<\/li>\n\n\n\n<li><em>f<\/em>(<em>x<\/em>) = 3<em>x<\/em><sup>2<\/sup> + 2<\/li>\n<\/ol>\n\n\n\n<ol type=\"A\">\n\t<li style=\"list-style:upper-latin;\">f(x) = x2 + 3<\/li>\n\t<li style=\"list-style:upper-latin;\">f(x) = 2&#215;2 + 3<\/li>\n\t<li style=\"list-style:upper-latin;\">f(x) = 2&#215;2 + 3<\/li>\n\t<li style=\"list-style:upper-latin;\">{2, -4}<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Daerah asal (P) = {1, 2, 3}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Daerah kawan (Q) = {5, 11, 21}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pasangan berurutan <em>f<\/em> = {(1, 5), (2, 11), (3, 21)}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mencari fungsi <em>f<\/em>, perhatikan cara berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(1, 5} = 2(1)<sup>2<\/sup> + 3 = 5<\/li>\n\n\n\n<li>(2, 11} = 2(2)<sup>2<\/sup> + 3 = 11<\/li>\n\n\n\n<li>(3, 21} = 2(3)<sup>2<\/sup> + 3 = 21<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, rumus fungsi <em>f<\/em> adalah <em>f<\/em>(<em>x<\/em>) = 2<em>x<\/em><sup>2<\/sup> + 3.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: B<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 3<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui fungsi <em>f<\/em> : <em>x<\/em> \ud83e\udc6a 3<em>x<\/em><sup>2<\/sup> untuk himpunan bilangan bulat. Jika <em>f<\/em>(<em>x<\/em>) = 27, nilai <em>x<\/em> yang memenuhi adalah \u2026.<\/p>\n\n\n\n<ol type=\"A\">\n\t<li style=\"list-style:upper-latin;\">{3, -3}<\/li>\n\t<li style=\"list-style:upper-latin;\">{3}<\/li>\n\t<li style=\"list-style:upper-latin;\">{1, -3}<\/li>\n\t<li style=\"list-style:upper-latin;\">{2, -4}<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui <em>f<\/em> (<em>x<\/em>): <em>x<\/em> \ud83e\udc6a 3<em>x<\/em><sup>2<\/sup>, artinya rumus fungsinya <em>f<\/em>(<em>x<\/em>) = 3<em>x<\/em><sup>2<\/sup>. Jika nilai <em>f<\/em>(<em>x<\/em>) = 3<em>x<\/em><sup>2<\/sup>, maka:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/tRkFOVdX5L5vXFnw4XYMI7LgthSA5JDRGULsTSxwWPQ19c3vT3O9TEXxmyCxda7qbQhfRd-ONGTrod76MpF97TbSLxACCT_9bXfxB-EwOXqyIFFOINA3tyyHK8PKxdW6ti4wE-J2Fbyk9pHgOU6qdE572hePP2vW_t6GyzXfJX3SI1RYlaeZ2bZm5FlStJRGgjISSmBTCA\" alt=\"\" width=\"77\" height=\"94\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai <em>x<\/em> yang memenuhi adalah {3, -3}.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: A<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 4<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Semua siswa SD Sukamaju mendapatkan nomor bangku ujian. Tidak ada satupun siswa yang memiliki nomor bangku sama. Relasi antara siswa dan nomor bangkunya termasuk dalam fungsi \u2026.<\/p>\n\n\n\n<ol type=\"A\">\n\t<li style=\"list-style:upper-latin;\">Surjektif<\/li>\n\t<li style=\"list-style:upper-latin;\">Relasi<\/li>\n\t<li style=\"list-style:upper-latin;\">Injeksi<\/li>\n\t<li style=\"list-style:upper-latin;\">Bijektif<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Semua siswa SD Sukamaju mendapatkan nomor bangku ujian yang berbeda. Artinya, tidak akan ada anak yang memiliki nomor bangku sama. Jika dinyatakan dalam bentuk relasi, anggota asal\/ domain (anak) tepat berpasangan satu-satu dengan anggota kawan\/ kodomain (nomor bangku). Relasi semacam ini disebut sebagai korespondensi satu-satu atau fungsi bijektif.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, relasi antara siswa dan nomor bangkunya termasuk dalam fungsi bijektif.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: D<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 5<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Sebuah tempat wisata memasang tarif masuk Rp10.000 setiap orang dan ditambah tarif parkir Rp5.000 untuk setiap kendaraan roda empat. Jika Ani datang ke tempat wisata tersebut bersama 3 rekannya menggunakan mobil, biaya yang harus ia bayarkan adalah \u2026.<\/p>\n\n\n\n<ol type=\"A\">\n\t<li style=\"list-style:upper-latin;\">Rp35.000<\/li>\n\t<li style=\"list-style:upper-latin;\">Rp40.000<\/li>\n\t<li style=\"list-style:upper-latin;\" rp45.000<=\"\" li=\"\">\n\t<\/li><li style=\"list-style:upper-latin;\">Rp50.000<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tarif parkir = Rp.5000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tarif masuk = Rp10.000\/orang<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Secara keseluruhan, tarif masuk tempat wisata dengan roda empat dinyatakan sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em> (<em>x<\/em>) = 10.000<em>x<\/em> + 5.000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jika Ani dan tiga rekannya (4 orang) masuk, uang yang harus dibayarkan adalah sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em> (<em>x<\/em>) = 10.000<em>x<\/em> + 5.000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 10.000(4) + 5.000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 40.000 + 5.000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 45.000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, biaya yang harus dibayarkan Ani adalah Rp45.000.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: C<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 6<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Farel melemparkan bola dari <em>rooftop<\/em> rumahnya. Gerak bola tersebut mengikuti persamaan <em>f<\/em>(<em>t<\/em>) = 10 \u2013 2<em>t<\/em> dengan <em>t<\/em> dalam s. Waktu yang diperlukan bola untuk sampai tanah adalah \u2026.<\/p>\n\n\n\n<ol type=\"A\">\n\t<li style=\"list-style:upper-latin;\">5 s<\/li>\n\t<li style=\"list-style:upper-latin;\">6 s<\/li>\n\t<li style=\"list-style:upper-latin;\">4 s<\/li>\n\t<li style=\"list-style:upper-latin;\">3 s<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Farel melemparkan bola dari <em>rooftop<\/em> rumahnya. Gerak bola tersebut mengikuti persamaan <em>f<\/em>(<em>t<\/em>) = 10 \u2013 2<em>t<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ditanya: <em>t<\/em> = \u2026?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawab:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Waktu yang dibutuhkan bola untuk sampai tanah yang ketinggiannya 0 m dirumuskan sebagai berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em>(<em>t<\/em>) = 10 \u2013 2<em>t<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2194 0 = 10 \u2013 2<em>t<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21942<em>t<\/em> = 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2194<em>t <\/em>= 5 s<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, waktu yang dibutuhkan bola untuk sampai tanah adalah 5 s.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: A<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 7<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui daerah kawan Q = {8, 12, 16, 20}. Jika <em>f<\/em>(<em>x<\/em>) = 2<em>x <\/em>+ 4, maka daerah asal P yang memenuhi adalah \u2026.<\/p>\n\n\n\n<ol type=\"A\">\n\t<li style=\"list-style:upper-latin;\">{2, 6, 8, 10}<\/li>\n\t<li style=\"list-style:upper-latin;\">{2. 4, 6, 8}<\/li>\n\t<li style=\"list-style:upper-latin;\">{1, 2, 3, 4}<\/li>\n\t<li style=\"list-style:upper-latin;\">{2,3,4,6}<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Daerah kawan Q = {8, 12, 16, 20}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>f<\/em>(<em>x<\/em>) = 2<em>x <\/em>+ 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ditanya: daerah asal P =\u2026?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mencari daerah asal, kamu harus mensubstitusikan setiap anggota Q pada rumus fungsinya.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>8 \ud83e\udc6a 8 = 2(<em>x<\/em>) + 4<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">4 = 2<em>x<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>x<\/em><\/strong><strong> = 2<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>12 \ud83e\udc6a 12 = 2(<em>x<\/em>) + 4<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">8 = 2<em>x<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>x<\/em><\/strong><strong> = 4<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>16 \ud83e\udc6a 16 = 2(<em>x<\/em>) + 4<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">12 = 2<em>x<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>x<\/em><\/strong><strong> = 6<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>20 \ud83e\udc6a 20 = 2(<em>x<\/em>) + 4<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">16 = 2<em>x<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>x<\/em><\/strong><strong> = 8<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai asal P yang memenuhi adalah P = {2, 4, 6, 8}.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: B<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 8<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui dua himpunan, yaitu himpunan S dan T. Anggota himpunan S merupakan bilangan ganjil antara 0 sampai 10. Sementara itu, anggota himpunan T adalah bilangan pangkat dua antara 1 sampai 10. Banyaknya fungsi yang mungkin dari himpunan S ke T adalah \u2026.<\/p>\n\n\n\n<ol type=\"A\">\n\t<li style=\"list-style:upper-latin;\">32<\/li>\n\t<li style=\"list-style:upper-latin;\">28<\/li>\n\t<li style=\"list-style:upper-latin;\">16<\/li>\n\t<li style=\"list-style:upper-latin;\">8<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">S = bilangan ganjil antara 0 sampai 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">T = bilangan berpangkat antara 1 sampai 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ditanya: banyaknya fungsi yang mungkin dari himpunan S ke T = \u2026?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawab:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">S = {1, 3, 5, 7, 9,}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>n<\/em>(S) = 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">T = {4, 9}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>n<\/em>(T) = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Banyaknya fungsi = <em>n<\/em>(T)<em><sup>n<\/sup><\/em><sup>(S)<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 2<sup>5<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 32<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, banyaknya fungsi yang mungkin dari himpunan S ke T adalah 32.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: A<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 9<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui himpunan pasangan berikut ini.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">K = {(1, a), (2, b), (3, c), (4, d)}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">L = {(1, a), (2, a), (3, b), (4, c)}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">M = {(1, c), (2, a), (3, b), (4, c)}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N = {(1, d), (2, c), (3, b), (4, a)}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Himpunan yang menunjukkan korespondensi satu-satu adalah \u2026.<\/p>\n\n\n\n<ol type=\"A\">\n\t<li style=\"list-style:upper-latin;\">K da L<\/li>\n\t<li style=\"list-style:upper-latin;\">M da N<\/li>\n\t<li style=\"list-style:upper-latin;\">K dan N<\/li>\n\t<li style=\"list-style:upper-latin;\">L dan M<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Korespondensi satu-satu atau fungsi bijektif adalah fungsi yang daerah asalnya tepat berpasangan dengan satu daerah kawan. Artinya, jumlah anggota asal harus sama dengan anggota kawan. Dari beberapa himpunan pada soal, diperoleh kesimpulan bahwa:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>K = {(1, a), (2, b), (3, c), (4, d)} \u2192 korespondensi satu-satu<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">L = {(1, a), (2, a), (3, b), (4, c)} \u2192 bukan korespondensi satu-satu karena dua daerah asal berpasangan dengan satu daerah kawan yang sama, yaitu (1, a) dan (2, a).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">M = {(1, c), (2, a), (3, b), (4, c)} \u2192 bukan korespondensi satu-satu karena dua daerah asal berpasangan dengan satu daerah kawan yang sama, yaitu (1, c) dan (4, c).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N = {(1, d), (2, c), (3, b), (4, a)} \u2192 korespondensi satu-satu<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, himpunan yang termasuk korespondensi satu-satu adalah K dan N.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: C<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 10<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Perhatikan diagram Venn berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/AjUOo41y_FGqKJBON3yK_N36cEjjUAje6moLvoXkJOtjV24uKiq46YYi-okuXV95N4JQTq0-FXvaclBtzAOHiSuTImTty-CqumhU47ct2VCI9FHvZOLxejL5Yjx6Q8pzdIrBKiiwAYNZB5lZZVEmBqmIyZQs7MGcFD1WJqaceJKk3RuLT-YmIwFacrIzZSqLea1gILt_Ug\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Fungsi yang tepat dari A ke B adalah \u2026.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. <em>f<\/em>(<em>x<\/em>) = 2<em>x<\/em><sup>3<\/sup><br>B. <em>f<\/em>(<em>x<\/em>) = <em>x<\/em><sup>2<\/sup><br>C. <em>f<\/em>(<em>x<\/em>) = <em>x<\/em><sup>3<\/sup><br>D. <em>f<\/em>(<em>x<\/em>) = <em>x<\/em><sup>3<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Perhatikan kembali diagram Venn berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/AjUOo41y_FGqKJBON3yK_N36cEjjUAje6moLvoXkJOtjV24uKiq46YYi-okuXV95N4JQTq0-FXvaclBtzAOHiSuTImTty-CqumhU47ct2VCI9FHvZOLxejL5Yjx6Q8pzdIrBKiiwAYNZB5lZZVEmBqmIyZQs7MGcFD1WJqaceJKk3RuLT-YmIwFacrIzZSqLea1gILt_Ug\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Relasi antara A dan B disebut korespondensi satu-satu. Hubungan antara kedua himpunan tersebut bisa dijabarkan seperti berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Untuk <em>x<\/em> = 2 \u2192 8 = 2<sup>3<\/sup><\/li>\n\n\n\n<li>Untuk <em>x<\/em> = 3 \u2192 27 = 3<sup>3<\/sup><\/li>\n\n\n\n<li>Untuk <em>x<\/em> = 4 \u2192 64 = 4<sup>3<\/sup><\/li>\n\n\n\n<li>Untuk <em>x<\/em> = 5 \u2192 125 = 5<sup>3<\/sup><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Artinya, <em>f<\/em>(<em>x<\/em>) = <em>x<\/em><sup>3<\/sup>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, fungsi yang tepat dari A ke B adalah <em>f<\/em>(<em>x<\/em>) = <em>x<\/em><sup>3<\/sup>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawaban: D<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog kali ini. Semoga bermanfaat, ya. Untuk melihat contoh soal lainnya, silahkan gabung bareng <a href=\"https:\/\/www.quipper.com\/id\/video\/\">Quipper Blog<\/a>. Bersama Quipper Blog belajar jadi lebih mudah dan menyenangkan. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, apakah kamu gemar bermain puzzle? Tentu kamu tahu bahwa setiap kepingan puzzle hanya bisa mengisi satu bentuk posisi dan tidak bisa digantikan&hellip;<\/p>\n","protected":false},"author":156447303,"featured_media":307664,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384865],"tags":[679386714],"ppma_author":[679386823,679386836],"class_list":["post-307648","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-matematika-kelas-8"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Kumpulan Contoh Soal Relasi dan Fungsi Lengkap dengan Jawaban dan Pembahasan - Quipper Blog<\/title>\n<meta name=\"description\" content=\"10 contoh soal ini bisa mempercapat kamu menguasai materi relasi dan fungsi. 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