Question

Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. f(x)=x−−√+2, g(x)=x2+9

Answer 1

We have the next functions

`\begin{gathered} f(x)=\sqrt[]{x}+2 \\ g(x)=x^2+9 \end{gathered}`

For f(g(x))

`f(g(x))=\sqrt[]{x^2+9}+2`

For g(f(x))

`\begin{gathered} g(f(x))=(\sqrt[]{x}+2)^2+9 \\ g(f(x))=x+4\sqrt[]{x}+4+9 \\ g(f(x))=x+4\sqrt[]{x}+13 \end{gathered}`

ANSWER

`f(g(x))=\sqrt[]{x^2+9}+2`
`g(f(x))=x+4\sqrt[]{x}+13`