Pertanyaan

Jika diketahui fungsi f ( x ) = 2 x − 7 , g ( x ) = x 2 + 5 , d an ( x ) 2 x 2 − 1. M aka ( f ∘ g ∘ h − 1 ) ( x ) =...

Jika diketahui fungsi $f (x) = 2 x - 7, g (x) = x^{2} + 5, d an (x) 2 x^{2} - 1. M aka (f \circ g \circ h^{- 1}) (x)$ =...

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Penyelesaian:

$h left parenthesis x right parenthesis equals 2 x squared minus 1 y equals 2 x squared minus 1 y plus 1 equals 2 x squared x equals square root of fraction numerator y plus 1 over denominator 2 end fraction end root h to the power of negative 1 end exponent equals square root of fraction numerator x plus 1 over denominator 2 end fraction end root$
$f left parenthesis x right parenthesis equals 2 x minus 7 space d a n space g left parenthesis x right parenthesis equals x squared plus 5 left parenthesis f ring operator g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals left parenthesis f ring operator left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis right parenthesis left parenthesis x right parenthesis m i s a l equals left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals p left parenthesis x right parenthesis left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals g open parentheses fraction numerator square root of x plus 1 end root over denominator 2 end fraction close parentheses equals open parentheses square root of fraction numerator x plus 1 over denominator 2 end fraction end root close parentheses squared plus 5 equals fraction numerator x plus 1 over denominator 2 end fraction plus 5 equals fraction numerator x plus 1 over denominator 2 end fraction plus 10 over 2 equals fraction numerator x plus 11 over denominator 2 end fraction$
$left parenthesis f ring operator left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis right parenthesis left parenthesis x right parenthesis equals open parentheses f ring operator p close parentheses left parenthesis x right parenthesis equals f open parentheses fraction numerator x plus 11 over denominator 2 end fraction close parentheses equals 2 open parentheses fraction numerator x plus 11 over denominator 2 end fraction close parentheses minus 7 equals x plus 11 minus 7 equals x plus 4$