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- In Exercises 13-14, find the domain of each function. 13. f(x) 3 (х +2)(х — 2) 14. g(x) (х + 2)(х — 2) In Exercises 15–22, let f(x) = x? – 3x + 8 and g(x) = -2x – 5.For Exercises 57–62, find and simplify f(x + h). (See Example 6) 59. f(x) = 7 – 3x 62. f(x) = x – 4x + 2 57. f(x) = -4x – 5x + 2 58. f(x) = -2x² + 6x – 3 60. f(x) = 11 – 5x² 61. f(x) = x' + 2x – 5In Exercises 16–22, show that the two functions are inverses of each other. 2 16. f(x) = 3x + 2 and g(x) = 3
- Each of Exercises 19–24 gives a formula for a function y = f(x). In each case, find f(x) and identify the domain and range of f¯1. 20. f(x) = x*, x > 0 22. f(x) = (1/2)x – 7/2 24. f(x) = 1/x³, x + 0 19. f(x) = x³ 21. f(x) = x³ + 1 23. f(x) = 1/x², x> 0 %3DExercises 103–110: Let the domain of f(x) be [-1,2] and the range be [0, 3 ]. Find the domain and range of the following. 103. f(x – 2) 104. 5/(x + 1) 105. -/(x) 106. f(x – 3) + 1 107. f(2x) 108. 2f(x – 1) 109. f(-x) 110. -2/(-x)In Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. 33. f(x) = V36(x + 2)² 34. f(x) = V81(x – 2)2 35. f(x) = V32(x + 2)³ 36. f(x) = V48(x – 2)³ 37. f(x) = V3x² – 6x + 3 38. f(x) = V5x2 – 10x + 5 %3D
- In Exercises 39–44, each function f(x) changes value when x changes from x, to xo + dx. Find a. the change Af = f(xo + dx) – f(xo); b. the value of the estimate df = f'(xo) dx; and c. the approximation error |Af – df|. y = f(x)/ Af = f(xo + dx) – f(x) df = f'(xo) dx (xo, F(xo)) dx Tangent 0| xo + dx 39. f(x) 3D х? + 2x, хо —D 1, 40. f(x) = 2x² + 4x – 3, xo = -1, dx = 0.1 41. f(x) = x³ - x, xo = 1, dx = 0.1 dx = 0.1 %3D 42. f(x) 3 х, Хо —D 1, dx %3D 0.1 43. f(x) — х 1, Хо —D 0.5, dx %3D0.1 44. f(x) 3D х3 — 2х + 3, Хо — 2, dx 3D 0.1Suppose that during the period 1990–2001, U.S. imports of pasta increased from 270 million pounds in 1990 (t = 0) by an average of 50 million pounds/year. (a) Use these data to express q, the annual U.S. imports of pasta (in millions of pounds), as a linear function of t, the number of years since 1990. q(t) = (b) Use your model to estimate U.S. pasta imports (in millions of pounds) in 2003, assuming the import trend continued.Suppose that during the period 1990–2001, U.S. imports of pasta increased from 300 million pounds in 1990 (t = 0) by an average of 35 million pounds/year. (a) Use these data to express q, the annual U.S. imports of pasta (in millions of pounds), as a linear function of t, the number of years since 1990. q(t) = (b)Use your model to estimate U.S. pasta imports (in millions of pounds) in 2006, assuming the import trend continued. _________million pounds
- Find the derivatives of the functions in Exercises 17–40. 20. f(t) t? + t – 21. Determine each value for the function f(x) = -4x + 7. a) f(0) d) f(- f(1/2) b) f(3) e) f(-2x) c) f(-1) f) f(3x)Exercises 3 and 4: Write f(x) in the general form f(x) = ax? + bx + c, and identify the leading coefficient. 3. f(x) = -2(x – 5)² + 1 4. f(x) = }(x + 1) - 2