3. Functions

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.

Find the domain of each function. f(x) = 2(x+5)

Without using paper and pencil, evaluate each expression given the following functions. $\text{ƒ}\left(x\right)=x+1$ and $g\left(x\right)=x^2$

(ƒg)(2)

Find the domain of each function. g(x) = 2/(x+5)

Without using paper and pencil, evaluate each expression given the following functions. $\text{ƒ}\left(x\right)=x+1$ and $g\left(x\right)=x^2$

$(\text{ƒ}\circ g)\left(2\right)$

Without using paper and pencil, evaluate each expression given the following functions. $\text{ƒ}\left(x\right)=x+1$ and $g\left(x\right)=x^2$

$(g\circ \text{ƒ})\left(2\right)$

Find the domain of each function. f(x) = 1/(x²+1) - 1/(x²-1)

Find the domain of each function. h(x) = 4/(3/x - 1)

Let $\text{ƒ}\left(x\right)=x^2+3$ and $g\left(x\right)=-2x+6$. Find each of the following. See Example 1.

$\left(\text{ƒ}g\right)(-3)$