Jika g(x)=x−1 dan (f∘g)(x)=4x−21+3x​, nilai f−1(1)=....

Pertanyaan

Jika dan , nilai ....

  1. size 14px 2

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Pembahasan

Jika dan ,

kita akan mencari f(x) terlebih dahulu dengan cara :

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

kita cari terlebih dahulu size 14px g to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px x size 14px right parenthesis

begin mathsize 14px style y equals x minus 1 y plus 1 equals x g to the power of negative 1 end exponent left parenthesis x right parenthesis equals x plus 1 end style

sedemikian sehingga :

size 14px left parenthesis size 14px f size 14px ring operator size 14px g size 14px ring operator size 14px g to the power of size 14px minus size 14px 1 end exponent size 14px right parenthesis size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals begin mathsize 14px style left parenthesis f ring operator g right parenthesis end style size 14px left parenthesis size 14px g 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 right parenthesis

                           begin mathsize 14px style equals open parentheses f ring operator g close parentheses left parenthesis x plus 1 right parenthesis equals fraction numerator 1 plus 3 left parenthesis x plus 1 right parenthesis over denominator 4 left parenthesis x plus 1 right parenthesis minus 2 end fraction equals fraction numerator 1 plus 3 x plus 3 over denominator 4 x plus 4 minus 2 end fraction equals fraction numerator 3 x plus 4 over denominator 4 x plus 2 end fraction end style

diperoleh begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 3 x plus 4 over denominator 4 x plus 2 end fraction end style. kita cari inversnya :

begin mathsize 14px style y equals fraction numerator 3 x plus 4 over denominator 4 x plus 2 end fraction y left parenthesis 4 x plus 2 right parenthesis equals 3 x plus 4 4 x y plus 2 y equals 3 x plus 4 4 x y minus 3 x equals negative 2 y plus 4 x left parenthesis 4 y minus 3 right parenthesis equals negative 2 y plus 4 x equals fraction numerator negative 2 y plus 4 over denominator 4 y minus 3 end fraction f to the power of negative 1 end exponent left parenthesis 1 right parenthesis equals fraction numerator negative 2 plus 4 over denominator 4 minus 3 end fraction equals 2 over 1 equals 2 end style

 jadi, jawabannya E

75

5.0 (7 rating)

Intan Latifa Putri Utoyo

Pembahasan lengkap banget Mudah dimengerti

Pertanyaan serupa

Jika g(x)=2x−1 dan (f∘g)(x)=2x+3 maka

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