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¢R~T~¢AL TH~NKING about the Lesson
1. Describe how to find the inverse relation of a relation given
by a set of ordered pairs. Give aft example.
2. Describe how to find the inverse relation of a relation given
by a~ equatio~ in x and y. Give an example.
3. Find an equation that represents the inverse of the function
f(x) = ~x - 4. Sketch the graphs of f and its inverse. Is the
inverse of f a function~
4. The gaphs of f(x) = -~x~ - 1 and the inverse of f are shown
at the ~i~t. Is the inverse of f a function of x? Explain.
S. How is the graph of a ~elation ~elated to the graph of its
6. Verify that/(x) = 2x + 4 and g(x) = ~x - 2 are inverses of
each other.
Chapter 6 ¯ Functions
In Exercises 15-22, write an equation for the inverse of the relation.
15. y=-3x+5
16. y=2x-3
17. y=x+4
19. y= 12K-6
20. y=-13x+6
18. y=-5x+9
22. y=9x- 14
21. y=4x-
In Exercises 23-30, sketch the function and its inverse in the same coordinate plane. Is the inverse a function of x?
25. fix) = 3x + 4
29. f(x) = -X~ - 4
24. f(x) = -x + 2
28, fix) = -x~ + 3
26. f(x) = 2Xz + 4
30. f(x) = ½x + 9
In Exercises 31-34, sketch the graph of the function. Use the graph of fto
decide whether the inverse of f is a function of x.
32. f(x) = -2xz- 1
33. f(x) = xz- 2
31. f(x)=x+ 1
in Exercises 35-40, verify that f and g are inverses of each other.
36. fix)=-x+4, g(x)=-x+4
38. f(x) = ½x + 2, g(x) = 2x - 4
40, fix)=-4x+8, g(x)=-¼x+2
41. [emperature Conversion The formula
to convert temperature in degrees Celsius
to temperature in degrees Fahrenheit is
For this formula, C is the input and F is
the output. Rewrite the formula so that F
is the input and C is the output.
Geometry The height h of an equilateral triangle with sides of length s is
h ~ Vgs.
Rewrite the~ formula so that the height is
the input and the length of the sides is the
’ Handfcap You belong to a bowling league in which each
handicap, H, is determined by his or her average, A, acto the following formula.
%o0 - A)
the bowler’s average is over 200, the handicap is 0.) Rewrite this
so that the handicap is the input and the average is the
I~ your handicap is 32, what is your average?
Tax In a state that has a 6% sales tax, the total cost,
?, of a taxable item that has a price of p is C = 0.06p + p. Rewrite
so that C is the input and p is the output.
6.3 ¯ Inverse Functions 303