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:

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

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:

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