Chapter 1.5, Problem 43E

Suppose that F ,(x) = f (x) and G ,(x) = g(x). Which of the following statements are true? Explain.   (a) If f = g, then F = G.(b) If F and G differ by a constant, then f = g.(c) If f and g differ by a constant, then F = G.

Estimate

Use Definition 0.10 to show that each pair of functions in Exercises 67–70 are inverses of each other. 1 2 67. f(x) =2 – 3x and g(x) = -x+ 3 68. f(x) = x² restricted to [0, 0) and g(x) = V 69. f(x) = and g(x) = 1+x 1-x 1 1 70. f(x) = and g(x) 2x 2x

Answer all a

Electrical Engineering For the given functions f x x^3 +2x^8 and g x = x^3, a) Determine with justification whether f x = 0 g(x) is true. b) Determine with justification whether g x = 0 f(x) is true.

Exercises 37-42: Complete the following for the function f. (a) Evaluate f(x) at the indicated values of x. (b) Find the domain of f. Use interval notation. 37. f(x) = 5 for x = -3, 1.5 38. f(x) = 4 - 5x for x = -5, 6 39. f(x) = x² – 3 for x= -10, a + 2 40. f(x) = x' - 3x for x = -10, a + 1 41. f(x) =4 for x = -3, a + 1 42. f(x) = Vx + 3 for x = 1, a - 3