$3. 3(y - 2)2 - 7 $4. (1 -t)2 - (1 - t) 1 - 2 In Exercises $5-$11, solve the equation for y. $9. x = Vy-2 88. * = 4y 1 -y $5. x = 3y -4 $6. 4x - 3y=7 $11. x = 5 -(2y) Sil ty -4 EXERCISES In Exercises 1-4, find and simplify the expression. 1. f (5x + 3) for f (x) = 2x -1. 2. f(x + 5) for f(x) =x2+3. In Exercises 17-20, use the graphs of f and g in Figure 2.30 to find the value of the expression. 3. f(3x - 1) for f(x) = x2+4x+6. 4. f (x - 3) for f (x) = 2x2 + x+5. In In Exercises 5-12, use f (x) = 3x - 1 and g(x) = 1 -x2. 5. f(8 (0) ) 6. 8(f (0) ) 7. 8(f (2) ) 8. f(8 ( 2 ) ) HOT 9. f(g(x)) 10. g(f (x) ) 11. f(f (x) ) 12. 8(8(x) ) -2-101234 Figure 2.39 In Exercises 13-16, use Table 2.22 to find the value of the 17. f(8(2)) 18. f(8(-1)) 19. 8(f(-1) 20. & (f(0) expression. In Exercises 21-23, give the meaning and units of the com- Table 2.22 posite function. m -4 -2 + O 21. A(f(t)), where r = f (t) is the radius, in centimeters, of a circle at time t minutes, and A(r) is the area, in square O centimeters, of a circle of radius / centimeters. C 22. R(f(p)), where Q = f(p) is the number of barrels of oil sold by a company when the price is p dollars/barrel 13. f(8(0)) 14. g(f(3)) 15. g(8(1)) 16. f(8(-4)) and R(Q) is the revenue earned in millions of dollars from a sale of Q barrels.94 Chapter 2 FUNCTIONS 23. C(A(d)), where A(d) is the area of a circular pizza with diameter d, and C(x) is the price of pizza with area x. 41. For k(x) = 4x - 10, evaluate k(3) and k- (14). In Exercises 24-28, give the meaning and units of the inverse function. (Assume f is invertible.) 42 . For h( x ) = * + 2 , evaluaten ( - 2 ) and h- (8 ) . 43. For g(x) = 2x3 - 1, evaluate & () and 8-' (-17). Table 2.2 24. P = f (1) is population in millions in year . 25 . T = f ( H ) is time in minutes to bake a cake at HOF . 44. Use the graph in Figure 2.40 to fill in the missing val- h(x) 26. N = f(t) is number of inches of snow in the first t days ues : of January . (a) f(0) =? (b) f(?) = 0 k(x) 27. x = C(w) is calories for w ounces of almonds. (c) f-(0) =? (d) f- ( ? ) =0 d inches. 28. c = P(d) is the price, in dollars, for a pizza of diameter In Problems 50-52, number of gallons feet. In Exercises 29-32, use the complete graph of the invertible 50. Find a formula 29. function f (x) shown to estimate the domain of f-1(y). 1.5 51. Interpret and e 30 52. Calculate the f (f-'(n)). Exp f ( ) 53. The daily cost 2.2 f ( x ) up to 500 miles -9- m is the number Figure 2.40 (a) Find the d b) Find a for 31. 32. y 54. Table 2.25 giv (a) Using the f ( x ) 45. Use the graph in Figure 2.41 to fill in the missing val. ues: (i) f(0) - NW A UI - NWAUC (a) f(0) =? (iii) f- (b) f(?) = 0 (b) How do t c) f-(0 ) = ? (d) f-1 ( ? ) = 0 one anoth tained the 1 2 3 4 5 6 12 3 456 to (i) and f (x ) Tab In Exercises 33-39, find the inverse function. 33. y = f(1) = 2t + 3 34. y = f(x) =3x-7 35. y = 8(x) =x3+1 36. Q = f(x) =x3+3 37. A = f (r) = mr2, r20 Problems 55-57 38. y = 8(s) = 1+- C = f(T), in dol consin, as a functi 39. P = f(x) = 7 3x Figure 2.41 ble 2.27 gives the 2x + 1 degrees Fahrenhe 40. For f(x) = 5x, evaluate f(4) and f-1(15). Table 2.2 PROBLEMS 46. The cost (in dollars) of producing x air conditioners is 48. Let f(a) be the cost in dollars of a pounds of organ. C = 1 C = 8(x) = 600 + 45x. Find a formula for g-(C). Granny Smith apples at Walmart in April 2017.5 Et Table 2.27 47. Table 2.23 gives values for d = f(v), where d, in me- plain what the following statements tell you. What ur ters, is the stopping distance for a car traveling at veloc- the units of each of the numbers? T = g(t ity u kilometers per hour. (a) f(2) = 4.44 (b) f(0.5) = 1.11 (a) Evaluate and interpret f(60). (c) f-1 ( 2.22 ) = 1 (d) f- (11.10) = 5 (b) Estimate f (70). (c) Evaluate and interpret f-1(70) 49. Values of two functions h and k are given in Table If possible, find: Table 2.23 (b) k(h(2)) (c) hikul v (km/hr) 20 30 40 50 60