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Finding Arithmetic Combinations of Functions In Exercises 5–12, find
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Precalculus (MindTap Course List)
- The function f(x) = 0.4x2 – 36x + 1000 models the number of accidents, f(x), per 50 million miles driven as a function of a driver's age, x, in years, for drivers from ages 16 through 74, inclusive. The graph of f is shown. Use the equation for f to solve Exercises 45–48. 1000 flx) = 0.4x2 – 36x + 1000 16 45 74 Age of Driver 45. Find and interpret f(20). Identify this information as a point on the graph of f. 46. Find and interpret f(50). Identify this information as a point on the graph of f. 47. For what value of x does the graph reach its lowest point? Use the equation for f to find the minimum value of y. Describe the practical significance of this minimum value. 48. Use the graph to identify two different ages for which drivers have the same number of accidents. Use the equation for f to find the number of accidents for drivers at each of these ages. Number of Accidents (per 50 million miles)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_forwardIn Exercises 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2 2. ƒ(x) = 1 - 2x3. F(x) = sqrt(5x + 10) 4. g(x) = sqrt(x2 - 3x)5. ƒ(t) = 4/3 - t6. G(t) = 2/t2 - 16arrow_forward
- In Exercises 53 and 54, find a Maclaurin∫series for f (x).arrow_forwardFind Arithmetic Combinations of Functions.Find (a) ( f + g)(x), (b) ( f − g)(x), (c) ( fg)(x), and (d) ( f/g)(x). What is the domain of f/g? f(x) = x2 − 4, g(x) = √(3 − x)arrow_forwardEvaluate each expression using the graphs of y = f(x) and y= g(x) shown below. a) (g o f)(4)= (Simplify your answer.) a) (go f)(4) b) (g o f)(0) c) (f o g)(3) d) (f o g)(4) b) (g o f)(0)= (Simplify your answer.) c) (fo g)(3) = (Simplify your answer.) Ay 8 d) (fo g)(4)= (Simplify your answer.) 16 (x)) = Aarrow_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_forwardReferring to the figure, evaluate g(f(g(0)))?arrow_forwardIn Exercises 1-8, find all real values of x such that f(x) = g(x).arrow_forward
- The graphs of two functions, f and g, are illustrated. Use the graphs to answer parts (a)–(f). y=g(x) |(2, 2) (4, 1) (6, 1) (6, 0) 22, 1) 2 (3, –2) (5, –2) (4, –3) (a) (f+ g)(2) (b) (f + g) (4) (c) (f – g) (6) (d) (g – f) (6) () ()(4) (e) (f•g)(2) 2.arrow_forwardFind Arithmetic Combinations of Functions.Find (a) ( f + g)(x), (b) ( f − g)(x), (c) ( fg)(x), and (d) ( f/g)(x). What is the domain of f/g? f(x) = x2 + 3, g(x) = 2x − 1arrow_forwardEvaluate each expression using the graphs of y= f(x) and y = g(x) shown below. (a) (g o f)( - 1) (b) (g o f)(0) (c) (f o g)(- 1) (d) (f o g)(4) ..... (a) (g o f)(- 1) = 8- (Simplify your answer.) 6- y= g{x} 2- -2 10 2 ]y = f(x) -4- .....arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage