In Problems 27–36, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x))
any values of x that need to be excluded.
= x. Give
27. f(x) = 3x + 4; g(x) =
(x- 4)
28. f(x) = 3 – 2x; g(x) = -(x – 3)
29. f(x) = 4x – 8; 8(x) = + 2
30. f(x) = 2x + 6; 8(x) = ;x - 3
31. f(x) = x' - 8; g(x)·
Vx + 8
32. f(x) = (x – 2)², 2; g(x) = Vĩ + 2
33. f(x) = ; 8(x) =
34. f(x) = x; g(x)
x - 5
2x + 3'
2x + 3
4x - 3
3x + 5
35. f(x)
*: 8(x) =
8(x)
36. f(x) =
1- 2x
x + 4
2 - x
1.7
82 CHAPTER 1 Graphs and Functions
In Problems 37-42, the graph of a one-to-one function f is given. Draw the graph of the inverse function f"1. For convenience (and as
a hint), the graph of y = x is also given.
37.
y= X
38.
39.
y =X
3
(1, 2),
(0, 1)
(-1,0)
(2. )
(2, 1)
(1, 0) 3 X
(0, -1)
-3
(-1, -1)
3 X
-3
(-2, -2)
(-2, -2)
-하
-하
-하
40.
41.
y = x
42.
y = X
(-2, 1).
-3
3 X
(1, -1)
In Problems 23–28, answer the questions about the given function.
x² + 2
26. f(x) =
x + 4
23. f(x) = 2x? - x - 1
(a) Is the point (-1, 2) on the graph of f?
(b) If x = -2, what is f(x)? What point is on the graph of f?
(c) If f(x) = -1, what is x? What point(s) are on the graph
of f?
(d) What is the domain of f?
(e) List the x-intercepts, if any, of the graph of f.
(f) List the y-intercept, if there is one, of the graph of f.
24. f(x) = -3x² + 5x
(a) Is the point (-1, 2) on the graph of f?
(b) If x = -2, what is f(x)? What point is on the graph
of f?
(c) If f(x) = -2, what is x? What point(s) are on the graph
of f?
(d) What is the domain of f?
(e) List the x-intercepts, if any, of the graph of f.
(f) List the y-intercept, if there is one, of the graph of f.
x + 2
(a) Is the point ( 1,) on the graph of f?
(b) If x = 0, what is f(x)? What point is on the graph of f?
(c) If f(x) =5. what is x? What point(s) are on the graph
of f?
(d) What is the domain of f?
(e) List the x-intercepts, if…
Chapter 7 Solutions
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