Pertanyaan

Diketahui fungsi f ( x ) = 8 x − 4 dan g ( x ) = 12 + 6 x . Maka tentukan: a. ( g ∘ f ) − 1 ( x ) b. ( g ∘ f ) − 1 ( 3 )

Diketahui fungsi $f (x) = 8 x - 4$ dan $g (x) = 12 + 6 x$ . Maka tentukan:

a. $(g \circ f)^{- 1} (x)$

b. $(g \circ f)^{- 1} (3)$

I. Ridha

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

.

Pembahasan

Diketahui: Ditanya: a. b. Jawab: a. Akan dicari fungsi komposisi dari terlebih dahulu. Didapat , fungsi inversnya: Jadi, . b. Akan disubtitusi nilai ke fungsi . Jadi, .

Diketahui:

Ditanya:

Jawab:

a. Akan dicari fungsi komposisi dari terlebih dahulu.

Didapat , fungsi inversnya:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell 48 x minus 12 end cell row y equals cell 48 x minus 12 end cell row cell 48 x end cell equals cell y plus 12 end cell row x equals cell fraction numerator y plus 12 over denominator 48 end fraction rightwards double arrow left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 12 over denominator 48 end fraction end cell end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x plus 12 over denominator 48 end fraction end cell end table end style$ .

b. Akan disubtitusi nilai ke fungsi .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 12 over denominator 48 end fraction end cell row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis 3 right parenthesis end cell equals cell fraction numerator 3 plus 12 over denominator 48 end fraction end cell row blank equals cell 15 over 48 end cell row blank equals cell 5 over 16 end cell end table end style$

Jadi, .