3. Functions

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

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

Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = 4x + 9 and g(x) = (x-9)/4

The functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = 2x + 3

Find the inverse of f(x)=(x−10)/(x+10).

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

Determine whether each pair of functions graphed are inverses.

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1.

(ƒ/g)(5)

The functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = (x +4)/(x-2)

Find ƒ+g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=6x+2

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒ/g)(-1)

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 functions f and g, (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=-6x+9,g\left(x\right)=5x+7$

Use the table to evaluate each expression, if possible.

$(\text{ƒ}+g)\left(1\right)$