Question

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

Answer 1

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)`