Pertanyaan

Jika f ( x ) = 3 x − 4 dan g ( x ) = 3 x − 4 1 , nilai ( f ∘ g ) − 1 ( − 2 ) = ....

Jika $f (x) = 3 x - 4$ dan $g (x) = \frac{1}{3 x - 4}$ , nilai $(f \circ g)^{- 1} (- 2) =$ ....

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Jika dan , akan kita cari fungsi komposisinya: kemudian, kita cari inversnya : jadi, jawabannya D

Jika dan ,

akan kita cari fungsi komposisinya:

$begin mathsize 14px style equals f open parentheses fraction numerator 1 over denominator 3 x minus 4 end fraction close parentheses equals 3 open parentheses fraction numerator 1 over denominator 3 x minus 4 end fraction close parentheses minus 4 equals fraction numerator 3 over denominator 3 x minus 4 end fraction minus fraction numerator 4 left parenthesis 3 x minus 4 right parenthesis over denominator 3 x minus 4 end fraction equals fraction numerator 3 minus 12 x plus 16 over denominator 3 x minus 4 end fraction equals fraction numerator 19 minus 12 x over denominator 3 x minus 4 end fraction end style$

kemudian, kita cari inversnya :

$size 14px y size 14px equals fraction numerator size 14px 19 size 14px minus size 14px 12 size 14px x over denominator size 14px 3 size 14px x size 14px minus size 14px 4 end fraction size 14px y size 14px left parenthesis size 14px 3 size 14px x size 14px minus size 14px 4 size 14px right parenthesis size 14px equals size 14px 19 size 14px minus size 14px 12 size 14px x size 14px 3 size 14px x size 14px y size 14px minus size 14px 4 size 14px y size 14px equals size 14px 19 size 14px minus size 14px 12 size 14px x size 14px 3 size 14px x size 14px y size 14px plus size 14px 12 size 14px x size 14px equals size 14px 19 size 14px plus size 14px 4 size 14px y size 14px x size 14px left parenthesis size 14px 3 size 14px y size 14px plus size 14px 12 size 14px right parenthesis size 14px equals size 14px 19 size 14px plus size 14px 4 size 14px y size 14px x size 14px equals fraction numerator size 14px 4 size 14px y size 14px plus size 14px 19 over denominator size 14px 3 size 14px y size 14px plus size 14px 12 end fraction size 14px left parenthesis size 14px f size 14px ring operator size 14px g size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px 4 size 14px x size 14px plus size 14px 19 over denominator size 14px 3 size 14px x size 14px plus size 14px 12 end fraction size 14px left parenthesis size 14px f size 14px ring operator size 14px g size 14px right parenthesis to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px minus size 14px 2 size 14px right parenthesis size 14px equals fraction numerator size 14px 4 size 14px left parenthesis size 14px minus size 14px 2 size 14px right parenthesis size 14px plus size 14px 19 over denominator size 14px 3 size 14px left parenthesis size 14px minus size 14px 2 size 14px right parenthesis size 14px plus size 14px 12 end fraction size 14px equals fraction numerator size 14px minus size 14px 8 size 14px plus size 14px 19 over denominator size 14px minus size 14px 6 size 14px plus size 14px 12 end fraction size 14px equals size 14px 11 over size 14px 6$

jadi, jawabannya D