6.Which equation defines a one-to-one function? Explain why the others are not, using spe-
cific examples.
A. B. C. D.
7.Only one of the graphs illustrates a one-to-one function. Which one is it? (See Example 2.)
A. B. C. D.
8.Concept Check If a function ƒ is one-to-one and the point lies on the graph of ƒ,
then which point mustlie on the graph of?
A. B. C. D.
If the function is one-to-one, find its inverse. See Examples 1–3.
- , 16. ,
Concept Check Let. We will see in the next section that this function is one-to-
one. Find each value, always working part (a) before part ( b).
ƒ 1 x 2 = 2 x
ƒ 1 x 2 =x^3 - 4 ƒ 1 x 2 =x^3 + 5
ƒ 1 x 2 = 3 x^2 + 2 ƒ 1 x 2 = 4 x^2 - 1
g 1 x 2 = 2 x- 3 xÚ 3 g 1 x 2 = 2 x+ 2 xÚ- 2
ƒ 1 x 2 = 2 x+ 4 ƒ 1 x 2 = 3 x+ 1
51 - 1, 3 2 , 1 2, 7 2 , 1 4, 3 2 , 1 5, 8 26 51 - 8, 6 2 , 1 - 4, 3 2 , 1 0, 6 2 , 1 5, 10 26
e1-1, 3 2 , 1 0, 5 2 , 1 5, 0 2 , a7, -
1
2
51 3, 6 2 , 1 2, 10 2 , 1 5, 12 26 bf
1 - p, q 2 1 - q, -p 2 1 p, -q 2 1 q, p 2
ƒ-^1
1 p, q 2
ƒ 1 x 2 =x ƒ 1 x 2 =x^2 ƒ 1 x 2 =|x| ƒ 1 x 2 =-x^2 + 2 x- 1
578 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions
- (a)
(b)
22. (a)
(b)
23. (a)
(b)
24. (a)
(b)ƒ-^1 a
1
4
b
ƒ 1 - 22
ƒ-^1112
ƒ 102
ƒ-^11162
ƒ 142
ƒ-^1182
ƒ 132
x
y
0 x
y
0
x
y
0
x
y
0
The graphs of some functions are given in Exercises 25 –30. (a)Use the horizontal line test to
determine whether the function is one-to-one. (b)If the function is one-to-one, then graph the
inverse of the function. ( Remember that if ƒis one-to-one and is on the graph of ƒ,then
is on the graph of .) See Example 4.
28. 29. 30.
1 b, a 2 ƒ-^1
1 a, b 2
x
y
3
0 3
x
y
–3
2
0
x
y
1
–1^0
x
y
–1
2
0 x
y
0
4
–2
x
y
02
5
