3. Functions & Graphs

Given the functions $f\(\left\)(x\(\right\))=\(\sqrt{x+4}\)$ and $g\(\left\)(x\(\right\))=\(\left\)(x-2\(\right\))^2-4$ find $\(\left\)(f\(\circ\) g\(\right\))\(\left\)(x\(\right\))$ and $\(\left\)(g\(\circ\) f\(\right\))\(\left\)(x\(\right\))$

Given the functions $f(x)=\(\frac{1}{x^2-2}\)$ and $g(x)=\(\sqrt{x+2}\)$ find $(f∘g)(x)$ and $(g\(\circ\) f)(x)$.

Given the functions $f(x)=x+3$ and $g(x)= x^2$ find $(f∘g)(2)$ and $(g∘f)(2)$.

Given the functions $f(x) = x^2$ and $g(x)=\(\sqrt{x-8}\)$ find $(f∘g)(x)$ and determine its domain.