Pertanyaan

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

Diketahui $f (x) = \frac{x - 2}{x + 2}$ dan $g (x) = 2 x + 2$ , maka $(f \circ g)^{- 1} (2) =$ ...

D. Entry

Master Teacher

Jawaban terverifikasi

Jawaban

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Pembahasan

Diketahui: Komposisi fungsi : Invers fungsi komposisi : Maka, fungsi invers adalah . Nilai : Sehingga, nilai dari adalah . Jadi, tidak ada pilihan jawaban yang tepat.

Diketahui:

$f left parenthesis x right parenthesis equals fraction numerator x minus 2 over denominator x plus 2 end fraction$
g left parenthesis x right parenthesis equals 2 x plus 2

Komposisi fungsi open parentheses f ring operator g close parentheses open parentheses x close parentheses :

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator open parentheses 2 x plus 2 close parentheses minus 2 over denominator open parentheses 2 x plus 2 close parentheses plus 2 end fraction end cell row blank equals cell fraction numerator 2 x over denominator 2 x plus 4 end fraction end cell end table$

Invers fungsi komposisi open parentheses f ring operator g close parentheses open parentheses x close parentheses :

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 2 x over denominator 2 x plus 4 end fraction end cell row y equals cell fraction numerator 2 x over denominator 2 x plus 4 end fraction end cell row cell y open parentheses 2 x plus 4 close parentheses end cell equals cell 2 x end cell row cell 2 x y plus 4 y end cell equals cell 2 x end cell row cell 2 x y minus 2 x end cell equals cell negative 4 y end cell row cell x open parentheses 2 y minus 2 close parentheses end cell equals cell negative 4 y end cell row x equals cell negative fraction numerator 4 y over denominator 2 y minus 2 end fraction end cell end table$

Maka, fungsi invers open parentheses f ring operator g close parentheses open parentheses x close parentheses adalah $open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals negative fraction numerator 4 x over denominator 2 x minus 2 end fraction$ .

Nilai open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses :

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell negative fraction numerator 4 x over denominator 2 x minus 2 end fraction end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses end cell equals cell negative fraction numerator 4 left parenthesis 2 right parenthesis over denominator 2 left parenthesis 2 right parenthesis minus 2 end fraction end cell row blank equals cell negative fraction numerator 8 over denominator 4 minus 2 end fraction end cell row blank equals cell negative 8 over 2 end cell row blank equals cell negative 4 end cell end table$

Sehingga, nilai dari open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses adalah negative 4 .

Jadi, tidak ada pilihan jawaban yang tepat.