Pertanyaan

Diketahui fungsi f : R → R d an g : R → R dengan f ( x ) = x − 6 x + 4 , x  = 6 dan g ( x ) = 2 x − 1 , maka ( f ∘ g ) − 1 ( x ) adalah ...

Diketahui fungsi $f : R \to R d an g : R \to R$ dengan $f (x) = \frac{x + 4}{x - 6}, x \neq = 6 dan g (x) = 2 x - 1$ , maka $(f \circ g)^{- 1} (x)$ adalah ...

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Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f left parenthesis 2 x minus 1 right parenthesis end cell row blank equals cell fraction numerator left parenthesis 2 x minus 1 right parenthesis plus 4 over denominator left parenthesis 2 x minus 1 right parenthesis minus 6 end fraction end cell row blank equals cell fraction numerator 2 x plus 3 over denominator 2 x minus 7 end fraction end cell row y equals cell fraction numerator 2 x plus 3 over denominator 2 x minus 7 end fraction end cell row cell y times left parenthesis 2 x minus 7 right parenthesis end cell equals cell 2 x plus 3 end cell row cell 2 x y minus 7 y end cell equals cell 2 x plus 3 end cell row cell 2 x y minus 2 end cell equals cell 7 y plus 3 end cell row cell x times left parenthesis 2 y minus 2 right parenthesis end cell equals cell 7 y plus 3 end cell row x equals cell fraction numerator 7 y plus 3 over denominator 2 y minus 2 end fraction end cell row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 7 x plus 3 over denominator 2 x minus 2 end fraction space. end cell end table end style$