Jika f(x)=2x+3 dan g(x)=3x−11​, maka (f∘g)−1(x)=

Pertanyaan

Jika dan , maka

F. Ayudhita

Master Teacher

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Jawaban

jawabannya A

Pembahasan

Pembahasan

Jika dan ,

Kita tentukan dulu fungsi komposisinya:

size 14px left parenthesis size 14px f size 14px ring operator size 14px g size 14px right parenthesis begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px f size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px f begin mathsize 14px style left parenthesis fraction numerator 1 over denominator 3 x minus 1 end fraction right parenthesis end style size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px 2 begin mathsize 14px style left parenthesis fraction numerator 1 over denominator 3 x minus 1 end fraction right parenthesis end style size 14px plus size 14px 3 size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals fraction numerator size 14px 2 over denominator size 14px 3 size 14px x size 14px minus size 14px 1 end fraction size 14px plus fraction numerator size 14px 3 size 14px left parenthesis size 14px 3 size 14px x size 14px minus size 14px 1 size 14px right parenthesis over denominator size 14px 3 size 14px x size 14px minus size 14px 1 end fraction size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals fraction numerator size 14px 2 size 14px plus size 14px 9 size 14px x size 14px minus size 14px 3 over denominator size 14px 3 size 14px x size 14px minus size 14px 1 end fraction size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals fraction numerator size 14px 9 size 14px x size 14px minus size 14px 1 over denominator size 14px 3 size 14px x size 14px minus size 14px 1 end fraction

maka begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style adalah

begin mathsize 14px style y equals fraction numerator 9 x minus 1 over denominator 3 x minus 1 end fraction y left parenthesis 3 x minus 1 right parenthesis equals 9 x minus 1 3 x y minus y equals 9 x minus 1 3 x y minus 9 x equals y minus 1 x left parenthesis 3 y minus 9 right parenthesis equals y minus 1 x equals fraction numerator y minus 1 over denominator 3 y minus 9 end fraction end style

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 x size 14px minus size 14px 1 over denominator size 14px 3 size 14px x size 14px minus size 14px 9 end fraction

Jadi jawabannya A

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Jika f(x)=3x+42x−1​ dan g(x)=2x+2​, maka nilai (f∘g)−1(−1)=...

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