Pertanyaan

Jika diketahui fungsi f ( x ) = 3 x − 2 , g ( x ) = 2 x + 1 , maka ( f − 1 ∘ g − 1 ∘ h − 1 ) ( x ) =....

Jika diketahui fungsi $f (x) = 3 x - 2, g (x) = 2 x + 1, maka (f^{- 1} \circ g^{- 1} \circ h^{- 1}) (x)$ =....

$fraction numerator x minus 60 over denominator 13 end fraction$
$fraction numerator x plus 30 over denominator 13 end fraction$
$fraction numerator x minus 30 over denominator 13 end fraction$
$fraction numerator x plus 13 over denominator 30 end fraction$
$fraction numerator x minus 13 over denominator 30 end fraction$

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Penyelesaian:

$f left parenthesis x right parenthesis equals 3 x minus 2 y equals 3 x minus 2 3 x equals y plus 2 left right double arrow x equals fraction numerator y plus 2 over denominator 3 end fraction f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 2 over denominator 3 end fraction$
$g left parenthesis x right parenthesis equals square root of 2 x plus 1 end root y equals square root of 2 x plus 1 end root y squared equals 2 x plus 1 2 x equals y squared minus 1 x equals fraction numerator y squared minus 1 over denominator 2 end fraction g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x squared minus 1 over denominator 2 end fraction$
$h left parenthesis x right parenthesis equals 5 x squared plus 2 y equals 5 x squared plus 2 y minus 2 equals 5 x squared x squared equals fraction numerator y minus 2 over denominator 5 end fraction x equals square root of fraction numerator y minus 2 over denominator 5 end fraction end root h to the power of negative 1 end exponent left parenthesis x right parenthesis equals square root of fraction numerator x minus 2 over denominator 5 end fraction end root$
$M i s a l space left parenthesis g to the power of negative 1 end exponent ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals p left parenthesis x right parenthesis left parenthesis g to the power of negative 1 end exponent ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals left parenthesis g to the power of negative 1 end exponent left parenthesis h to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis right parenthesis equals g to the power of negative 1 end exponent open parentheses square root of fraction numerator x minus 2 over denominator 5 end fraction end root close parentheses squared minus 1 equals fraction numerator begin display style fraction numerator x minus 2 over denominator 5 end fraction end style minus begin display style 5 over 5 end style over denominator 2 end fraction equals fraction numerator x minus 7 over denominator 5 end fraction.1 half equals fraction numerator x minus 7 over denominator 10 end fraction p left parenthesis x right parenthesis equals fraction numerator x minus 7 over denominator 10 end fraction left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals left parenthesis f to the power of negative 1 end exponent ring operator p right parenthesis left parenthesis x right parenthesis left parenthesis f to the power of negative 1 end exponent left parenthesis p right parenthesis right parenthesis left parenthesis x right parenthesis equals f to the power of negative 1 end exponent open parentheses fraction numerator x minus 7 over denominator 10 end fraction close parentheses equals fraction numerator begin display style fraction numerator x minus 7 over denominator 10 end fraction end style plus 2 over denominator 3 end fraction equals fraction numerator x plus 13 over denominator 10 end fraction.1 third equals fraction numerator x plus 13 over denominator 30 end fraction$