Pertanyaan

Jika diketahui fungsi f ( x ) = 4 x + 5 2 x − 3 d an g ( x ) = x − 1 , maka ( f − 1 ∘ g − 1 ) ( − 2 ) = ...

Jika diketahui fungsi $f (x) = \frac{2 x - 3}{4 x + 5} d an g (x) = x - 1, maka (f^{- 1} \circ g^{- 1}) (- 2)$ = ...

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A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Penyelesaian:

$f left parenthesis x right parenthesis equals fraction numerator 2 x minus 3 over denominator 4 x plus 5 end fraction f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 5 x minus 3 over denominator 4 x minus 2 end fraction g left parenthesis x right parenthesis equals square root of x minus 1 end root y equals square root of x minus 1 end root y squared equals x minus 1 x equals y squared plus 1 g to the power of negative 1 end exponent left parenthesis x right parenthesis equals x squared plus 1 left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals f to the power of negative 1 end exponent left parenthesis g to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis equals f to the power of negative 1 end exponent left parenthesis x squared plus 1 right parenthesis equals fraction numerator negative 5 left parenthesis x squared minus 8 over denominator 4 x squared plus 2 end fraction left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis 2 right parenthesis equals fraction numerator negative 5 left parenthesis negative 2 right parenthesis squared minus 8 over denominator 4 left parenthesis negative 2 right parenthesis squared plus 2 end fraction equals fraction numerator negative 5 left parenthesis 4 right parenthesis minus 8 over denominator 4 left parenthesis 4 right parenthesis plus 2 end fraction equals fraction numerator negative 20 minus 8 over denominator 8 plus 2 end fraction equals fraction numerator negative 28 over denominator 10 end fraction equals negative 2 comma 8$

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