Question

Find F o g o h F(x)= 1/x , g(x)=x^3 , h(x)=x+2

Answer 1

The Composite Function

Given the functions:

`\begin{gathered} f(x)=(1)/(x) \\ g(x)=x^3 \\ h(x)=x+2 \end{gathered}`

Find f o g o h.

The composite function of three components is:

`(f\circ g\circ h)(x)=f(g(h(x)))`

First, find g o h:

`(g\circ h)(x)=g(h(x)))=(x+2)^3`

Now substitute the result above into f:

`\begin{gathered} (f\circ g\circ h)(x)=f((x+2)^3) \\ (f\circ g\circ h)(x)=(1)/((x+2)^3) \end{gathered}`