Intermediate Algebra (11th edition)

To find let

Let.

Add.

Find by letting

(b) Solve for y. (Step 1)

Add 4y. Subtract 5.

y= y=ƒ 1 x 2 (Step 2)

x- 5

4

, so ƒ 1 x 2 =

1

4

x-

5

4

x- 5 = 4 y

x- 4 y= 5

ƒ 1 a 2 x= a: ƒ 1 a 2 = a^2 + 1.

ƒ 1 - 22 = 5

ƒ 1 - 22 = 4 + 1 1 - 222 =- 21 - 22

ƒ 1 - 22 = 1 - 222 + 1 x=- 2

ƒ 1 x 2 =x^2 + 1

ƒ 1 - 22 , x=-2.

192 CHAPTER 3 Graphs, Linear Equations, and Functions

a-b

c =

a

c-

b

c

NOW TRY
EXERCISE 5
Refer to the function graphed
in FIGURE 47.

(a)Find

(b)For what value of xis
ƒ 1 x 2 =2?

ƒ 1 - 12.

x

y

0

2

4

24

y = f(x)

FIGURE 47

(c) For what value of xis

Since we want the value of xthat corresponds to Locate 5 on

the y-axis. See FIGURE 49. Moving across to the graph of ƒ and down to the x-axis gives

x= 4 .Thus, ƒ 142 = 5 ,which corresponds to the ordered pair 1 4, 5 2. NOW TRY

ƒ 1 x 2 =y, y= 5.

ƒ 1 x 2 =5?

x

y

0

2

5

4

2 4

y = f(x)

FIGURE 49

If a function ƒ is defined by an equation with xand y, and yis not solved for x,

use the following steps to find ƒ 1 x 2.

Finding an Expression for

Step 1 Solve the equation for y.

Step 2 Replace ywith ƒ 1 x 2.

ƒ 1 x 2

Writing Equations Using Function Notation

Rewrite each equation using function notation Then find and

(a)

This equation is already solved for y, so we replace

ƒ 1 x 2 =x^2 + 1 y=ƒ 1 x 2

y with ƒ 1 x 2.

y=x^2 + 1

ƒ 1 x 2. ƒ 1 - 22 ƒ 1 a 2.

EXAMPLE 6

NOW TRY ANSWERS

5. (a) 0 (b) 1

Finding Function Values from a Graph

Refer to the function graphed in FIGURE 47.

(a)Find.

Locate 3 on the x-axis. See FIGURE 48. Moving up to the graph of ƒ and over to

the y-axis gives 4 for the corresponding y-value. Thus, , which corresponds

to the ordered pair.

(b)Find.

Refer to FIGURE 48to see that ƒ 102 = 1.

ƒ 102

1 3, 4 2

ƒ 132 = 4

ƒ 132

EXAMPLE 5

FIGURE 48

x

y

0

1

2

4

243

y = f(x)