Pertanyaan

Diketahui fungsi f : R → R dan g : R → R dirumuskan dengan f ( x ) = 2 x − 1 dan g ( x ) = 2 − x x + 3 , x  = 2. Fungsi invers dari ( f ∘ g ) ( x ) adalah = ....

$Diketahui fungsi f : R \to R dan g : R \to R dirumuskan dengan f (x) = 2 x - 1 dan g (x) = \frac{x + 3}{2 - x}, x \neq = 2. Fungsi invers dari (f \circ g) (x) adalah = ....$

$left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 2 x plus 4 over denominator x plus 3 end fraction comma x not equal to negative 3$
$left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 2 x minus 4 over denominator x plus 3 end fraction comma x not equal to negative 3$
$left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 2 x plus 4 over denominator x minus 3 end fraction comma x not equal to 3$
$left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 3 x minus 2 over denominator 2 x plus 2 end fraction comma x not equal to negative 1$
$left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 3 x minus 2 over denominator negative 2 x plus 2 end fraction comma x not equal to 1$

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Pembahasan

$left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals straight f left parenthesis straight g left parenthesis straight x right parenthesis right parenthesis left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals straight f open parentheses fraction numerator straight x plus 3 over denominator 2 minus straight x end fraction close parentheses left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals 2 open parentheses fraction numerator straight x plus 3 over denominator 2 minus straight x end fraction close parentheses minus 1 left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals fraction numerator 2 straight x plus 6 over denominator 2 minus straight x end fraction minus 1 left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals fraction numerator 2 straight x plus 6 minus 1 left parenthesis 2 minus straight x right parenthesis over denominator 2 minus straight x end fraction left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals fraction numerator 3 straight x plus 4 over denominator 2 minus straight x end fraction equals fraction numerator 3 straight x plus 4 over denominator negative straight x plus 2 end fraction Invers space dari space straight h left parenthesis straight x right parenthesis equals fraction numerator ax plus straight b over denominator cx plus straight d end fraction space adalah space straight h to the power of negative 1 end exponent left parenthesis straight x right parenthesis equals fraction numerator negative dx plus straight b over denominator cx minus straight a end fraction Sehingga space invers space dari space left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals fraction numerator 3 straight x plus 4 over denominator negative straight x plus 2 end fraction space adalah left parenthesis straight f ring operator straight g right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis equals fraction numerator negative 2 straight x plus 4 over denominator negative straight x minus 3 end fraction left parenthesis straight f ring operator straight g right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis equals fraction numerator 2 straight x minus 4 over denominator straight x plus 3 end fraction$

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