3. Functions

Exercises 123–125 will help you prepare for the material covered in the next section. Solve for y : x = 5/y + 4

Find a. (fog) (2) b. (go f) (2) f(x) = 4-x, g(x) = 2x² +x+5

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

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

ƒ(x)=3x+4, g(x)=2x-5

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

Find (f+g)(−3).

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

Find

a. (fog) (x)

b. (go f) (x)

c. (fog) (2)

d. (go f) (2).

f(x) = 2x, g(x) = x+7

Express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x).

h(x) = (3x − 1)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

Given the functions $f\(\left\)(x\(\right\))=\(\sqrt{x+4}\)$ and $g\(\left\)(x\(\right\))=\(\left\)(x-2\(\right\))^2-4$ find $\(\left\)(f\(\circ\) g\(\right\))\(\left\)(x\(\right\))$ and $\(\left\)(g\(\circ\) f\(\right\))\(\left\)(x\(\right\))$

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

Determine whether the given functions are inverses. ƒ= {(2,5), (3,5), (4,5)}; g = {(5,2)}

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

Graph f+g.

Find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2).

f(x) = 2x-3, g(x) = (x+3)/2

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

(ƒ-g)(1)