¢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 inverse? 6. Verify that/(x) = 2x + 4 and g(x) = ~x - 2 are inverses of each other. 302 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 F=~G+32. 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. 2 Rewrite the~ formula so that the height is the input and the length of the sides is the output. ’ 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