Finding Compositions of Functions In Exercises 29–34, find
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Precalculus
- Which of the functions graphed in Exercises 1–6 are one-to-one, and which are not?arrow_forwardIn Exercises15–36, find the points of inflection and discuss theconcavity of the graph of the function. f(x)=\frac{6-x}{\sqrt{x}}arrow_forwardGraphing Inverse Functions Each of Exercises 11–16 shows the graph of a function y = ƒ(x).Copy the graph and draw in the line y = x. Then use symmetry withrespect to the line y = x to add the graph of ƒ -1 to your sketch. (It isnot necessary to find a formula for ƒ -1.) Identify the domain andrange of ƒ -1.arrow_forward
- Give an example of functions f and g such that f ∘ g = g ∘ f and f(x) ≠ g(x).arrow_forwardIn Exercises 59–62, sketch the graph of the given function. What is the period of the function?arrow_forwardFind the composition of functions, if it exists. f = {(-4, 1), (-2, 4), (0, 5), (2, 6), (4, 8)} g = {(-1, -3), (0, 2), (1, 4), (2, 5), (3, 7)} h = {(-3, -5), (-1, -1), (1, 1), (3, 5)} 62. (fo g)(x) 63. (go f(x) 64. (go h)(x) 65. (ho g)(x) 66. (fo h)(x) 67. (ho f)(x) This page was Choices for 62-67: A) {(-1, -3), (1, 4)} B) {(5, 2), (6, 5)} C) {(-3, 7), (2, 0)} D) {(0, 6), (1, 8)} E) {(-4, 2), (0, 7)} AB) {(4, 1), (5, 7)} AC) {(-4, 4)} AD) {(-1, -5)} AE) {(-4, 1)} BC) Does not existarrow_forward
- Use the given graphs of f and g to evaluate each expression, or if the expression is undefined, enter UNDEFINED. (a) f(g(2)) = (b) g(f(0)) = (c) (f ∘ g)(0) = (d) (g ∘ f)(6) = (e) (g ∘ g)(-2) = (f) (f ∘ f)(4)arrow_forwardFind the functions (a) f ° g , (b) g ° f , (c) f ° f , and(d) g °g and their domains.arrow_forwardGraphing: In Exercises 69–76, graph each function, not by plotting points, but by starting with the graph of one of the standard functions presented in Figures 1.14–1.17 and applying an appropriate transformation.arrow_forward
- Consider the following functions. f={(1,-2),(0,-3),(3,-2),(4,-2)} and g(x)={(-3,1),(-1,2),(2,2),(3,-2)} Find (f+g)(3) Find (f-g)(3) Find (fg)(3) Find (f/g)(3)arrow_forwardIn Exercises 1-8, find all real values of x such that f(x) = g(x).arrow_forwardLet f= {(1,2), (1, -1)} and g = {(1, -3), (2, -1),(-4,-3)}. Find g - f and its domain.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage