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

Jika dan  , maka  ....

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F. Ayudhita

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Jika dan , kita menggunakan sifat invers fungsi komposisi : kita cari dulu fungsi komposisinya kemudian kita cari inversnya : jadi, jawabannya E

Jika dan  ,

kita menggunakan sifat invers fungsi komposisi :

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

kita cari dulu 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 open parentheses fraction numerator 2 x over denominator x plus 1 end fraction close parentheses equals open parentheses fraction numerator 2 x over denominator x plus 1 end fraction close parentheses plus 1 equals fraction numerator 2 x over denominator x plus 1 end fraction plus fraction numerator x plus 1 over denominator x plus 1 end fraction equals fraction numerator 3 x plus 1 over denominator x plus 1 end fraction end style

kemudian kita cari inversnya :

begin mathsize 14px style y equals fraction numerator 3 x plus 1 over denominator x plus 1 end fraction y x plus y equals 3 x plus 1 y x minus 3 x equals 1 minus y x left parenthesis y minus 3 right parenthesis equals 1 minus y x equals fraction numerator 1 minus y over denominator y minus 3 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 minus x over denominator x minus 3 end fraction end style

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 1 size 14px minus size 14px x over denominator size 14px x size 14px minus size 14px 3 end fraction size 14px equals fraction numerator size 14px x size 14px minus size 14px 1 over denominator size 14px 3 size 14px minus size 14px x end fraction

jadi, jawabannya E

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Diketahui f ( x ) = x − 6 x + 4 ​ , x  = 6 dan g ( x ) = 2 x − 1 . Rumus ( f ∘ g ) − 1 ( x ) = ....

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