Section 10.4Inverseof a Function 573In Exercises 23–28, nd the inverse of the function. Then graph the function and its inverse. (See Example 4.)23. f (x) 4x2, x ≥ 0 24. f (x) 1 — 25 x2, x ≤ 025. f (x) x2 + 10, x ≤ 026. f (x) 2x2 + 6, x ≥ 027.f (x) 1 — 9 x2 + 2, x ≥ 0 28. f (x) 4x2 8, x ≤ 0In Exercises 29–32, use the Horizontal Line Test to determine whether the inverse of f is a function.29. 30.422xy46224466f(x) ∣2x + 8∣ 22424xyf(x) x 1 331. 32. 2322xy22xf(x) x3 2122xyf(x) x2 3In Exercises 33–42, determine whether the inverse of f isa function. Then nd the inverse. (See Example 5.)33. f (x) √— x + 3 34. f (x) √— x 5 35. f (x) √— 2x 6 36. f (x) √— 4x + 1 37. f (x) 3 √— x 8 38. f (x) 1 — 4 √— 5x + 2 39. f (x) √— 3x + 5 2 40. f (x) 2 √— x 7 + 641. f (x) 2x2 42. f (x) x 43. ERROR ANALYSIS Describe and correct the error in nding the inverse of the function f (x) 3x + 5. y = 3x 5 y − 5 = 3x y − 5 — 3 = xThe inverse of f is g(x) = y − 5 — 3, or g(x)= y — 3 − 5 — 3 .✗
44. ERROR ANALYSIS Describe and correct the error in nding and graphing the inverse of the function f (x) √— x 3 . y = √— x − 3 x = √— y − 3 x2 = y − 3 x2 3 = yThe inverse of f is g(x) = x2 3.✗
2622xy45. MODELING WITH MATHEMATICS The euro is the unit of currency for the European Union. On a certain day, the number E of euros that could be obtained for D U.S. dollars was represented by the formula shown.E 0.74683DSolve the formula for D. Then nd the number of U.S. dollars that could be obtained for 250 euros on that day.46. MODELING WITH MATHEMATICS A crow is ying at a height of 50 feet when it drops a walnut to break it open. The height h (in feet) of the walnut above ground can be modeled by h16t2+50, where t is the time (in seconds) since the crow dropped the walnut. Solve the equation for t. After how many seconds will the walnut be 15 feet above the ground?50 ftMATHEMATICAL CONNECTIONS In Exercises 47 and 48, s is the side length of an equilateral triangle. Solve the formula for s. Then evaluate the new formula for the given value.hsss 47. Height: h √— 3 s — 2; h 16 in. 48. Area: A √— 3 s2 — 4; A 11 ft2