Given f(x)=x+2 and g(x)=4-x^2 find the following (g o f)(x)

Dlowe asked Apr 15, 2023

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Dlowe asked Apr 15, 2023

by Dlowe

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26 votes

Given functions are

$\begin{gathered} f(x)=x+2 \\ g(x)=4-x^2 \end{gathered}$

Then,

$\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(x+2) \\ =4-(x+2)^2 \\ =4-(x^2+4x+4) \\ =4-x^2-4x-4 \\ =-(x^2+4x) \end{gathered}$

Thus,

$(g\circ f)(x)=-(x^2+4x)$

Jzqa answered Apr 19, 2023

by Jzqa

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