2. Graphs & Functions

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

(A) $\(\left\)(f\(\circ\) g\(\right\))\(\left\)(x\(\right\))$ and

(B)$\(\left\)(g\(\circ\) f\(\right\))\(\left\)(x\(\right\))$.

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

(A) $(f\circ g)\left(x\right)$ and

(B) $(g\(\circ\) f)(x)$.

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

(A) $(f\circ g)\left(2\right)$ and

(B) $(g\circ f)\left(2\right)$.

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

Decomposition of Functions Practice 5