3. Functions

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

(ƒ/g)(2)

Find f−g and determine the domain for each function. f(x) = √x, g(x) = x − 4

Find fg and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 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.

$\text{ƒ}\left(x\right)=-x^2$

Determine whether each function graphed or defined is one-to-one.

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=1-x

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=-2x+5

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) = 3/(x-4) and g(x) = (3/x) + 4

Find the domain of each function. f(x) = √(24 - 2x)

In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. f(g(1))

Let $\text{ƒ}\left(x\right)=\text{√}(x-2)$ and $g\left(x\right)=x^2$. Find each of the following, if possible. the domain of $\text{ƒ○}g$

Use the graphs of f and g to solve Exercises 83–90.

Find the domain of ƒ + g.

In Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range of f and ƒ¯¹. f(x)=2x-1

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

$\text{ƒ}\left(x\right)=x+2,g\left(x\right)=x^4+x^2-4$

Find a. (fog) (x) b. (go f) (x). f(x) = √x, g(x) = x − 1