Pertanyaan

Jika f ( x ) = 3 x + 4 2 x − 1 d an g ( x ) = 2 x + 2 , maka ni l ai ( f ∘ g ) − 1 ( − 1 ) =...

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

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Penyelesaian:

$f left parenthesis x right parenthesis equals fraction numerator 2 x minus 1 over denominator 3 x plus 4 end fraction space d a n space g left parenthesis x right parenthesis equals fraction numerator x plus 2 over denominator 2 end fraction left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis equals f open parentheses fraction numerator x plus 5 over denominator 2 end fraction close parentheses equals 2 fraction numerator open parentheses begin display style fraction numerator x plus 5 over denominator 2 end fraction end style close parentheses minus 1 over denominator x open parentheses begin display style fraction numerator x plus 5 over denominator 2 end fraction end style close parentheses plus 4 end fraction equals fraction numerator x plus 5 minus 1 over denominator begin display style fraction numerator 3 x plus 15 plus 8 over denominator 2 end fraction end style end fraction equals fraction numerator x plus 4 over denominator begin display style fraction numerator 3 x plus 23 over denominator 2 end fraction end style end fraction equals fraction numerator 2 x plus 8 over denominator 3 x plus 23 end fraction left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative d x plus b over denominator c x minus a end fraction equals fraction numerator negative 23 plus 8 over denominator 3 x minus 2 end fraction left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis equals fraction numerator negative 23 left parenthesis negative 1 right parenthesis plus 8 over denominator 3 left parenthesis negative 1 right parenthesis minus 2 end fraction equals fraction numerator 23 plus 8 over denominator negative 3 minus 2 end fraction equals negative 31 over 5$