Finding Compositions of Functions In Exercises 29–34, find
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Precalculus (MindTap Course List)
- In Exercises15–36, find the points of inflection and discuss theconcavity of the graph of the function. f(x)=\frac{6-x}{\sqrt{x}}arrow_forwardf -8 f - g In Exercises 51–52, find (x) and the domain of h h 51. f(x) = 3x + 4x2 – x – 4,g(x) = -5x + 22x? – 28x – 12, h(x) = 4x + 1 52. f(x) = x + 9x? – 6x + 25, g(x) = -3x³ + 2x² – 14x + 5, h(x) = 2x + 4arrow_forwardFinding Limits of Differences When x u tHFind the limits in Exercises 86–90. (Hint: Try multiplying and dividing by the conjugate.)arrow_forward
- Give an example of functions f and g such that f ∘ g = g ∘ f and f(x) ≠ g(x).arrow_forwardFinding Arithmetic Combinations ofFunctions In Exercises 5–12, find(a) ( f + g)(x), (b) ( f − g)(x), (c) ( fg)(x), and(d) ( fg)(x). What is the domain of fg?5. f(x) = x + 2, g(x) = x − 26. f(x) = 2x − 5, g(x) = 2 − x7. f(x) = x2, g(x) = 4x − 58. f(x) = 3x + 1, g(x) = x2 − 169. f(x) = x2 + 6, g(x) = √1 − x10. f(x) = √x2 − 4, g(x) = x2x2 + 111. f (x) = xx + 1, g(x) = x312. f(x) = 2x, g(x) = 1x2 − 1arrow_forwardDecomposing a Composite FunctionIn Exercises 49–56, find two functions f andg such that ( f ∘ g)(x) = h(x). (There are manycorrect answers.)49. h(x) = (2x + 1)2 50. h(x) = (1 − x)351. h(x) = √3 x2 − 4 52. h(x) = √9 − x53. h(x) = 1x + 2 54. h(x) = 4(5x + 2)255. h(x) = −x2 + 34 − x256. h(x) = 27x3 + 6x10 − 27xarrow_forward
- Find 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_forwardIn Exercises 59–62, sketch the graph of the given function. What is the period of the function?arrow_forwardFinding Values for Which f(x) = g(x)In Exercises 43–46, find the value(s) of x forwhich f(x) = g(x).43. f(x) = x2, g(x) = x + 244. f(x) = x2 + 2x + 1, g(x) = 5x + 1945. f(x) = x4 − 2x2, g(x) = 2x246. f(x) = √x − 4, g(x) = 2 − xarrow_forward
- In 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. What is the domain of g - f? (Use a comma to separate your answers.)arrow_forward4. Working with functions. In this question, we will explore various properties of functions. You may want to review the basic definitions and terminology introduced on pages 15–16 of the course notes. Then, read the following definitions carefully. Definition: A function f : A → B is one-to-one iff no two elements of A have the same image. Symbol- ically, Va1, a2 E A, f(a1) = f(a2) → a1 = a2. (3) Definition: A function f: A → B is onto iff every element of B is the image of at least one element from A. Symbolically, VbE В, За Е А, f (a) — b. (4) Definition: For all functions f : A → B and g : B → C, their composition is the function g o f : A → C defined by: Va e A, (go f)(a) = g(f(a)). (5) (b) Give explicit, concrete definitions for two functions f1, f2 : Z → Z† such that: i. f2 is onto but not one-to-one, ii. fi is one-to-one but not onto, and prove that each of your functions has the desired properties.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage