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Diberikan f(x)=3x+1 dan  (f∘g)(x)=6x−2. Nilai g−1(5)=....

Pertanyaan

Diberikan dan  . Nilai ....

  1. 1

     

  2. 2

  3. 3

  4. 4

  5. 5

N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

Jawaban terverifikasi

Pembahasan

Diberikan dan  .

dengan menggunakan konsep :

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

maka kita cari dulu invers dari f(x):

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

kita komposisikan :

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

                         begin mathsize 14px style equals f to the power of negative 1 end exponent left parenthesis 6 x minus 2 right parenthesis equals fraction numerator left parenthesis 6 x minus 2 right parenthesis minus 1 over denominator 3 end fraction equals fraction numerator 6 x minus 3 over denominator 3 end fraction equals 2 x minus 1 end style

kita cari invers dari g(x) = 2x - 1 :

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

size 14px g to the power of size 14px minus size 14px 1 end exponent size 14px left parenthesis size 14px 5 size 14px right parenthesis size 14px equals fraction numerator size 14px 5 size 14px plus size 14px 1 over denominator size 14px 2 end fraction size 14px equals size 14px 3

Nilai 3

jadi, jawaban yang benar adalah C.

76

5.0 (4 rating)

Pertanyaan serupa

Diketahui f(x)=2x+1 dan (f∘g)(x+1)=−2x2−4x−1. Nilai dari g−1(−2) sama dengan ....

28

1.0

Jawaban terverifikasi

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