3. Functions

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\surd x,g\left(x\right)=\frac{1}{(x+5)}$

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

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 and g(x) = -x

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.

$\text{ƒ}\left(x\right)=1-x^2$

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) = x³ +2

Given functions f and g, find (ƒ∘g)(x) and its domain. ƒ(x)=1/(x-2), g(x)=1/x

Find f/g and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15

Find fg and determine the domain for each function. f(x) = 2 + 1/x, g(x) = 1/x

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

$\text{ƒ}\left(x\right)=8x+12,g\left(x\right)=3x-1$

Find the inverse of f(x) = x³ + 2

Use the table to evaluate each expression, if possible.

$(f-g)\left(3\right)$

Determine whether each function graphed or defined is one-to-one. y = 2x³ - 1

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 off and ƒ¯¹. f(x) = x³ − 1

Find fg and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = 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.

$(\text{ƒ}-g)\left(4\right)$