Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.6 - Combinations of Functions: Composite Functions - 2.6 Exercises - Page 219: 15

Answer

(f - g)(0) = 5

Work Step by Step

The notation (f - g)(0) can be rewritten as f(0) - g(0). Solving by subtracting the functions then evaluating at 0 will yield the same result as evaluating each function and then subtracting. In this question: f(x) = x + 3 g(x) = $x^{2}$ - 2 Method 1: Subtract the functions then evaluate First we want to subtract the two functions. The new function will be called h(x). h(x) = f(x) - g(x) h(x) = (x + 3) - ($x^{2}$ - 2) h(x) = x + 3 - $x^{2}$ + 2 Combine like variables to get: h(x) = -$x^{2}$ + x + 5 Evaluate at x = 0: h(0) = -$(0)^{2}$ + 0 + 5 = 5 Method 2: Evaluate the functions and then subtract First we want to evaluate f(x) at x = 0: f(0) = 0 + 3 = 3 Then we want to evaluate g(x) at x = 0: g(0) = $(0)^{2}$ - 2 = -2 Subtract the numbers together: (f - g)(0) = 3 - (-2) = 5 Using both methods (f - g)(0) = 5
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