3. Functions

Find a. (fog) (x) b. the domain of f o g.

f(x) = √x, g(x) = x − 2

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

If $f\left(x\right)=3x$ and $g\left(x\right)=x+5$, find ${(f\circ g)}^{-1}\left(x\right)$ and $(g^{-1}\circ f^{-1})\left(x\right)$.

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

ƒ(x)=√(4x-1), 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.

$\text{ƒ}\left(x\right)=\text{√}x,g\left(x\right)=x+3$

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) = 1/x

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

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

Find (g-f) (-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)=3x+8 and g(x) = (x-8)/3

Find all values of x satisfying the given conditions. f(x) = 2x − 5, g(x) = x² − 3x + 8, and (ƒ o g) (x) = 7.

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5.

$(\text{ƒ}\circ g)(-2)$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. ƒ(x)=√x, g(x)=x-1

Find f−g and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)

Determine whether each pair of functions graphed are inverses.

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.

$\text{ƒ}\left(x\right)=-4x+2$

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) = ∛x + 1