9
Chapter 1: Algebra Review
22. Use the horizontal line test to determine
which of the following functions is a oneto-one function and therefore has an
inverse.
(A) y = x
2
– 4
(B) y = x
2
– 4, x ≥ 0
(C) y = x
2
– 4, –2 ≤ x ≤ 8
(D) y = x
2
– 4, –12 ≤ x ≤ 6
(E) y = x
2
– 4, –5.3 ≤ x ≤ 0.1
23. Use the horizontal line test to determine
which of the following functions is a oneto-one function and therefore has an
inverse.
(A) y = x
4
+ 3x
2
– 7
(B) y
x
=
+
4
3
(C) y = cos x
(D) y = sin x
(E) y = tan
−1 
x
Find Inverses Algebraically
24–29 Find the inverse of the one-to-one function
algebraically.
24. f
 
(x) = 4 – 5x
25. f
 
(x) = x
2
– 4x, x ≥ 2
26. f x
x
( ) =
−
8 5
17. x y z x y z
4 8 5
3
7 4 10
3
18.
8
3 6
3
10 14
5
14 14
7
x y x y
x y
Writing Exponents Using
Radical Notation
19–20 Convert between exponential and radical
notation.
19. Convert 4
1 3 3 8 1 4 5 12
x y z
to radical notation.
(Note: The final answer can have more than
one radical sign.)
20. Convert 4
2
3
4
5
x y z to exponential notation.
The Horizontal Line Test
21–23 Use the horizontal line test to identify one-toone functions.
21. Use the horizontal line test to determine
which of the following functions is a oneto-one function and therefore has an
inverse.
(A) y = x
2
+ 4x + 6
(B) y
x
=
−
2
1
(C) y x
= 1
2
(D) y = 3x + 8
(E) y
x
=
−
25
2