Jika f(x)=2x−5 dan g(x)=3x+4, maka  (f−1∘g−1)(−5)=.....

Pertanyaan

Jika dan , maka  .....

  1. 5

  2. 4

  3.  3

  4. 2

  5. 1undefined

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Pembahasan

Jika dan ,

menggunakan konsep :

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

kita cari dulu fungsi komposisinya

begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals g left parenthesis f left parenthesis x right parenthesis right parenthesis end style

                begin mathsize 14px style equals g left parenthesis 2 x minus 5 right parenthesis equals 3 left parenthesis 2 x minus 5 right parenthesis plus 4 equals 6 x minus 15 plus 4 equals 6 x minus 11 end style

kemudian kita cari inversnya :

begin mathsize 14px style y equals 6 x minus 11 y plus 11 equals 6 x fraction numerator y plus 11 over denominator 6 end fraction equals x open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 11 over denominator 6 end fraction open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis negative 5 right parenthesis equals fraction numerator negative 5 plus 11 over denominator 6 end fraction equals 6 over 6 equals 1 end style

maka  1

jadi, jawabannya E

63

4.0 (4 rating)

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Jika f(x)=3x−4 dan g(x)=3x−41​, nilai (f∘g)−1(−2)=....

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