3. Functions

Use the definition of inverses to determine whether ƒ and g are inverses.

$f\left(x\right)=-4x+2,g\left(x\right)=-\frac{1}{4}x-2$

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

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

$(\text{ƒ}\circ g)\left(2\right)$

For the pair of functions defined, find (ƒ/g)(x). Give the domain of each. See Example 2.

ƒ(x)=2x^2-3x, g(x)=x^2-x+3

Determine whether each function graphed or defined is one-to-one. y = -1 / x+2

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) = ∛(x − 4) and g(x) = x³ +4

Which graphs in Exercises 96–99 represent functions that have inverse functions?

Use the graph to evaluate each expression. See Example 3(a).

(ƒg)(0)

Use the graph to evaluate each expression. See Example 3(a).

(ƒ-g)(-1)

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$\text{ƒ}\left(x\right)=x^2-4x+2$

For the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2.

ƒ(x)=2x^2-3x, g(x)=x^2-x+3

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)

Determine whether each function graphed or defined is one-to-one. y = 2(x+1)² - 6

Use the definition of inverses to determine whether ƒ and g are inverses. f(x) = x+1/x-2, g(x) = 2x+1/x-1