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

Pertanyaan

Jika size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px x over denominator size 14px x size 14px minus size 14px 1 end fractiondan size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px x size 14px plus size 14px 1, nilai begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 2 right parenthesis equals end style....

  1. size 14px minus size 14px 2

  2. size 14px minus size 14px 1 

  3. size 14px 0 

  4. size 14px 1 

  5. size 14px 2

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Pembahasan

Jika size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px x over denominator size 14px x size 14px minus size 14px 1 end fractiondan size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px x size 14px plus size 14px 1,

maka kita tentukan dahulu fungsi komposisinya :

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

                begin mathsize 14px style equals f left parenthesis x plus 1 right parenthesis equals fraction numerator left parenthesis x plus 1 right parenthesis over denominator left parenthesis x plus 1 right parenthesis minus 1 end fraction equals fraction numerator x plus 1 over denominator x end fraction end style

kemudian kita cari inversnya :

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

jadi, jawabannya D

47

5.0 (4 rating)

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Diketahui fungsi f dan g adalah fungsi bijektif yang ditentukan dengan f(x)=2x+5 dan g(x)=x−2. Tentukan: f.

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