10. Relations and Functions

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

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

Given the functions $f\left(x\right)=x+3$ and $g\left(x\right)=x^2$, find $(f\circ g)\left(2\right)$ and $(g\circ f)\left(2\right)$.

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