Ok, so
Given:
[tex]\begin{gathered} f(x)=\sqrt[]{x}-6 \\ g(x)=x^2+5 \end{gathered}[/tex]
We want to find (fog)(x) and (gof)(x).
First, let's find (fog)(x).
This is:
[tex](fog)(x)=f(g(x))=f(x^2+5)[/tex]
So we're going to evaluate f in (x2 + 5).
[tex]f(x^2+5)=\sqrt[]{x^2+5}-6[/tex]
Now, let's find (gof)(x). This is:
[tex](gof)(x)=g(f(x))=g(\sqrt[]{x}-6)_{}[/tex]
So we're going to evaluate g in the function f.
[tex]g(\sqrt[]{x}-6)=(\sqrt[]{x}-6)^2+5[/tex]
