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

Pertanyaan

Jika dan , nilai ....

F. Ayudhita

Master Teacher

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Pembahasan

Pembahasan

Jika dan ,

akan kita cari fungsi komposisinya:

begin mathsize 14px style left parenthesis f ring operator g right parenthesis 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 open parentheses fraction numerator 1 over denominator 3 x minus 4 end fraction close parentheses equals 3 open parentheses fraction numerator 1 over denominator 3 x minus 4 end fraction close parentheses minus 4 equals fraction numerator 3 over denominator 3 x minus 4 end fraction minus fraction numerator 4 left parenthesis 3 x minus 4 right parenthesis over denominator 3 x minus 4 end fraction equals fraction numerator 3 minus 12 x plus 16 over denominator 3 x minus 4 end fraction equals fraction numerator 19 minus 12 x over denominator 3 x minus 4 end fraction end style

kemudian, kita cari inversnya :

size 14px y size 14px equals fraction numerator size 14px 19 size 14px minus size 14px 12 size 14px x over denominator size 14px 3 size 14px x size 14px minus size 14px 4 end fraction size 14px y size 14px left parenthesis size 14px 3 size 14px x size 14px minus size 14px 4 size 14px right parenthesis size 14px equals size 14px 19 size 14px minus size 14px 12 size 14px x size 14px 3 size 14px x size 14px y size 14px minus size 14px 4 size 14px y size 14px equals size 14px 19 size 14px minus size 14px 12 size 14px x size 14px 3 size 14px x size 14px y size 14px plus size 14px 12 size 14px x size 14px equals size 14px 19 size 14px plus size 14px 4 size 14px y size 14px x size 14px left parenthesis size 14px 3 size 14px y size 14px plus size 14px 12 size 14px right parenthesis size 14px equals size 14px 19 size 14px plus size 14px 4 size 14px y size 14px x size 14px equals fraction numerator size 14px 4 size 14px y size 14px plus size 14px 19 over denominator size 14px 3 size 14px y size 14px plus size 14px 12 end fraction 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 4 size 14px x size 14px plus size 14px 19 over denominator size 14px 3 size 14px x size 14px plus size 14px 12 end fraction 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 minus size 14px 2 size 14px right parenthesis size 14px equals fraction numerator size 14px 4 size 14px left parenthesis size 14px minus size 14px 2 size 14px right parenthesis size 14px plus size 14px 19 over denominator size 14px 3 size 14px left parenthesis size 14px minus size 14px 2 size 14px right parenthesis size 14px plus size 14px 12 end fraction size 14px equals fraction numerator size 14px minus size 14px 8 size 14px plus size 14px 19 over denominator size 14px minus size 14px 6 size 14px plus size 14px 12 end fraction size 14px equals size 14px 11 over size 14px 6

jadi, jawabannya D

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