SECTION 5.2 One-to-One Functions; Inverse Functions 291 24. x y 2 3 23 25. x y 3 3 23 26. y 3 3 23 x In Problems 27–34, find the inverse of each one-to-one function. State the domain and the range of each inverse function. 27. Atlanta, GA Boston, MA Las Vegas, NV Miami, FL Los Angeles, CA Location Annual Precipitation (inches) 49.7 43.8 4.2 61.9 12.8 Source: currentresults.com 28. Star Wars: The Force Awakens Avengers: Endgame Avatar Black Panther Avengers: Infinity War Title Domestic Gross (millions) $937 $858 $761 $700 $679 Source: boxofficemojo.com, September 2019 29. 30 40 50 Age $27.50 $42.00 $105.00 Monthly Cost of Life Insurance Source: ramseysolutions.com 30. Virginia Nevada Tennessee Texas State 2.8% 5.1% 3.1% 4.0% Unemployment Rate Source: United States Bureau of Labor Statistics, April, 2024 31. ( ) ( ) ( ) ( ) ( ) { } − − − − 3,5 , 2,9 , 1,2 , 0,11 , 1, 5 32. ( ) ( ) ( ) ( ) ( ) { } − − − 2,2, 1,6, 0,8, 1, 3, 2,9 33. ( ) ( ) ( ) ( ) ( ) { } − − − 2, 1 , 3, 2 , 10, 0 , 1, 9 , 2, 4 34. ( ) ( ) ( ) ( ) ( ) { } − − − − 2, 8, 1, 1, 0,0, 1,1, 2,8 In Problems 35–40, the graph of a one-to-one function f is given. Draw the graph of the inverse function −f .1 35. x y 3 23 3 y 5 x (1, 2) (0, 1) (21, 0) (22, 22) 23 36. x y 3 23 3 y 5 x ( (1, 0) (0, 21) (22, 22) 23 1 – 2 2, ) 37. x y 3 23 23 3 y 5 x (2, 1) (21, 21) 38. x y 3 23 23 3 y 5 x (22, 1) (1, 21) 39. x y 3 23 23 3 y 5 x 40. x y 2 22 22 2 y 5 x In Problems 41–50, verify that the functions f and g are inverses of each other by showing that ( ) ( ) = f g x x and ( ) ( ) = g f x x. Give any values of x that need to be excluded from the domain of f and the domain of g. 41. ( ) ( ) ( ) = + = − f x x g x x 3 4; 1 3 4 42. f x x g x x 3 2 ; 1 2 3 ( ) ( ) ( ) = − = − − 43. ( ) ( ) = − = + f x x g x x 4 8; 4 2 44. ( ) ( ) = + = − f x x g x x 2 6; 1 2 3
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