In Problems 1–18 use Definition 7.1.1 to find
2.
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FIRST CRSE.IN DIFF.EQUAT..-ACCESS
- In Problems 23–30, use the given zero to find the remaining zeros of each function. 23. f(x) = x - 4x² + 4x – 16; zero: 2i 24. g(x) = x + 3x? + 25x + 75; zero: -5i 25. f(x) = 2x* + 5x + 5x? + 20x – 12; zero: -2i 26. h(x) = 3x4 + 5x + 25x? + 45x – 18; zero: 3i %3D 27. h(x) = x* – 9x + 21x? + 21x – 130; zero: 3 - 2i 29. h(x) = 3x³ + 2x* + 15x³ + 10x2 – 528x – 352; zero: -4i 28. f(x) = x* – 7x + 14x2 – 38x – 60; zero:1 + 3i 30. g(x) = 2x – 3x* – 5x – 15x² – 207x + 108; zero: 3iarrow_forward6. If f (x) = x - 2, then f (x + h) -f (x) h a. -1 b. 1 c. 0arrow_forward1. Give the definition of each of the following (a) Z+ (b) F (Z+, R) (c) A (f)(x) (d) x (3) (e) x(-3)arrow_forward
- * 1.3 • If f(x) = 1. D; = R Rf = {1,0} 2. D; = [1,00) Rf = [0, c0) 3. D; = R R; = {1,–1} 4. D; = [1,00) R; = {1,0} then, %3D %3D %3Darrow_forward2.2 Deffetrentiate the following: 3x +1 a) f (x) = 2x + 5 b) S(x) = (emcot x) (8x – 1)2 c) f (x) = (3x – 1)? d) f(x) = x*arrow_forwardEstimate R3, M3, and L6 over [0, 1.5] for the function in Figure 17. 0.5 1.0 15 FIGURE 17 2.arrow_forward
- In Problems 27–36, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x)) any values of x that need to be excluded. = x. Give 27. f(x) = 3x + 4; g(x) = (x- 4) 28. f(x) = 3 – 2x; g(x) = -(x – 3) 29. f(x) = 4x – 8; 8(x) = + 2 30. f(x) = 2x + 6; 8(x) = ;x - 3 31. f(x) = x' - 8; g(x)· Vx + 8 32. f(x) = (x – 2)², 2; g(x) = Vĩ + 2 33. f(x) = ; 8(x) = 34. f(x) = x; g(x) x - 5 2x + 3' 2x + 3 4x - 3 3x + 5 35. f(x) *: 8(x) = 8(x) 36. f(x) = 1- 2x x + 4 2 - x 1.7 82 CHAPTER 1 Graphs and Functions In Problems 37-42, the graph of a one-to-one function f is given. Draw the graph of the inverse function f"1. For convenience (and as a hint), the graph of y = x is also given. 37. y= X 38. 39. y =X 3 (1, 2), (0, 1) (-1,0) (2. ) (2, 1) (1, 0) 3 X (0, -1) -3 (-1, -1) 3 X -3 (-2, -2) (-2, -2) -하 -하 -하 40. 41. y = x 42. y = X (-2, 1). -3 3 X (1, -1)arrow_forwardto STUDENTS of 5さ WHAT FUNCTION =C(x) =arrow_forward2. Determine the inverse of each function, then state its domain and range.arrow_forward
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