Roboguru

Diketahui fungsi . Jika daerah hasil  adalah . Daerah asal  adalah ....

Pertanyaan

Diketahui fungsi begin mathsize 14px style y equals f left parenthesis x right parenthesis equals 3 x plus 5 end style. Jika daerah hasil begin mathsize 14px style f end style adalah begin mathsize 14px style R subscript f equals open curly brackets right enclose y minus 13 less or equal than y less than 17 comma space y element of R close curly brackets end style. Daerah asal undefined adalah ....

  1. begin mathsize 14px style open curly brackets right enclose x minus 6 less or equal than x less than 4 comma space x element of R close curly brackets end style 

  2. begin mathsize 14px style left curly bracket right enclose x minus 6 less than x less or equal than 4 comma space x element of R right curly bracket end style 

  3. begin mathsize 14px style left curly bracket right enclose x minus 4 less or equal than x less or equal than 6 comma space x element of R right curly bracket end style 

  4. size 14px left curly bracket right enclose size 14px x size 14px minus size 14px 4 size 14px less or equal than size 14px x size 14px less than size 14px 6 size 14px comma size 14px space size 14px x size 14px element of size 14px R size 14px right curly bracket 

  5. size 14px left curly bracket right enclose size 14px x size 14px minus size 14px 4 size 14px less than size 14px x size 14px less or equal than size 14px 6 size 14px comma size 14px space size 14px x size 14px element of size 14px R size 14px right curly bracket 

Pembahasan Soal:

Diketahui:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 3 x plus 5 end cell row cell R subscript f end cell equals cell left curly bracket right enclose y minus 13 less or equal than y less than 17 comma space y element of R right curly bracket end cell end table end style 

maka dapat ditentukan daerah asal fungsi tersebut sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell negative 13 end cell row cell negative 13 end cell equals cell 3 x plus 5 end cell row cell 3 x end cell equals cell negative 18 end cell row x equals cell fraction numerator negative 18 over denominator 3 end fraction end cell row x equals cell negative 6 end cell row blank blank blank row cell f left parenthesis x right parenthesis end cell equals 17 row 17 equals cell 3 x plus 5 end cell row cell 3 x end cell equals 12 row x equals cell 12 over 3 end cell row x equals 4 end table end style 

Dengan demikian diperoleh daerah asal fungsi tersebut adalah begin mathsize 14px style D subscript f equals open curly brackets right enclose x minus 6 less or equal than x less than 4 comma space x element of R close curly brackets end style.

Jadi, jawaban yang benar adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 April 2021

Tonton video penjelasan konsepnya

Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved