In Problems 9–34, find f′(x) and simplify.
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- 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_forwardIn Problems 23–28, answer the questions about the given function. x² + 2 26. f(x) = x + 4 23. f(x) = 2x? - x - 1 (a) Is the point (-1, 2) on the graph of f? (b) If x = -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -1, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. 24. f(x) = -3x² + 5x (a) Is the point (-1, 2) on the graph of f? (b) If x = -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -2, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. x + 2 (a) Is the point ( 1,) on the graph of f? (b) If x = 0, what is f(x)? What point is on the graph of f? (c) If f(x) =5. what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if…arrow_forwardIn Problems 93–104, graph each polynomial function. 93. f(x) = x + 2r? - 5x - 6 94. f(x) = x' + &r? + 11x – 20 95. f(x) = 2x –x² + 2r – 1 96. f(x) = 2r + x² + 2x + 1 97. f(x) = x* + x² - 2 98. f(x) = x - 3x² – 4 %3D %3D 99. f(x) = 4x* + 7x? – 2 100. f(x) = 4xr + 15x? - 4 101. f(x) = x* + x³ - 3x² - x + 2 %3D %3D %3D 102. f(x) = x* - x - 6r? + 4x + 8 103. f(x) 4x5 - 8x - x + 2 104. f(x) = 4xs + 12x - x - 3arrow_forward
- 2. Let P(t) represent the population of Los Angeles t years after 1900. (a) Interpret P(10) = 319, 198 in words. P(10) - Р(0) (b) Given that P(0) = 102, 479 and P(10) = 319, 198, calculate and interpret 10 – 0 in words. (c) of Los Angeles reached 200,000. Set up an equation that could be used to find how many years after 1900 the populationarrow_forwardIn Problems 13–24, use the graph of the function f given.arrow_forwardLET'S PROVE IT! Direction: Determine if the given function is continuous and differentiable at the indicated values of x. Show your solutions on a separate sheet of paper.arrow_forward
- In Problems 11–20, for the given functions f and g. find: (a) (f° g)(4) (b) (g•f)(2) (c) (fof)(1) (d) (g ° g)(0) \ 11. f(x) = 2x; g(x) = 3x² + 1 12. f(x) = 3x + 2; g(x) = 2x² – 1 1 13. f(x) = 4x² – 3; g(x) = 3 14. f(x) = 2x²; g(x) = 1 – 3x² 15. f(x) = Vx; 8(x) = 2x 16. f(x) = Vx + 1; g(x) = 3x %3D 1. 17. f(x) = |x|; g(x) = 18. f(x) = |x – 2|: g(x) x² + 2 2 x + 1 x² + 1 19. f(x) = 3 8(x) = Vĩ 20. f(x) = x³/2; g(x) = X + 1'arrow_forwarddr 1. J(x-3)(x-2)arrow_forwardto STUDENTS of 5さ WHAT FUNCTION =C(x) =arrow_forward
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