3. Functions

Graph the inverse of each one-to-one function.

Which graphs in Exercises 29–34 represent functions that have inverse 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)

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

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 $g\left(x\right)=x^2$

$(g\circ \text{ƒ})\left(2\right)$

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒ+g)(3)

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)