Question

Let f(x) = v= -6 and g(x) = 22 +5.(fog)(x) =m(gof)(x) =

Answer 1

Ok, so

Given:

`\begin{gathered} f(x)=\sqrt[]{x}-6 \\ g(x)=x^2+5 \end{gathered}`

We want to find (fog)(x) and (gof)(x).

First, let's find (fog)(x).

This is:

`(fog)(x)=f(g(x))=f(x^2+5)`

So we're going to evaluate f in (x2 + 5).

`f(x^2+5)=\sqrt[]{x^2+5}-6`

Now, let's find (gof)(x). This is:

`(gof)(x)=g(f(x))=g(\sqrt[]{x}-6)_{}`

So we're going to evaluate g in the function f.

`g(\sqrt[]{x}-6)=(\sqrt[]{x}-6)^2+5`