Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Precalculus 1.5** **HW4** **Instructions:** Find the following: (a) \((f + g)(x)\), (b) \((f - g)(x)\), (c) \((f \cdot g)(x)\), (d) \(\left(\frac{f}{g}\right)(x)\). What is the domain of (d)? 1) \(f(x) = 3x - 6\), \(g(x) = 3 - x\) 2) \(f(x) = \frac{x}{x - 2}\), \(g(x) = x^3 + 1\) Evaluate the indicated function for \(f(x) = x^2 - 2\) and \(g(x) = x - 1\) algebraically. 3) \((f - g)(2)\) 4) \(\left(\frac{f}{g}\right)(t - 2)\) Find (a) \((f \circ g)(x)\) and (b) \((g \circ f)(x)\) 5) \(f(x) = x^4 - 4\), \(g(x) = \sqrt[4]{x + 4}\) 6) \(f(x) = x^2 + 9\), \(g(x) = \sqrt{x}\) Use the graphs of \(f\) and \(g\) to evaluate the functions: 7) (a) \((f \circ g)(1)\) (b) \((f \circ g)(4)\) 8) (a) \((f \circ g)(1)\) (b) \((g \circ f)(3)\) **Graphs Description:** - **Graph of \(f(x)\):** - The graph shows a V-shaped curve resembling an absolute value function. - It consists of points \((1, 2)\), \((2, 0)\), \((3, 2)\), and \((4, 3)\). - **Graph of \(g(x)\):** - The graph illustrates a downward-sloping linear function. - It includes points \((1, 3)\), \((2, 2)\), \((3, 1)\), and \((4, 0)\). Both graphs use a standard
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Transcribed Image Text:**Precalculus 1.5** **HW4** **Instructions:** Find the following: (a) \((f + g)(x)\), (b) \((f - g)(x)\), (c) \((f \cdot g)(x)\), (d) \(\left(\frac{f}{g}\right)(x)\). What is the domain of (d)? 1) \(f(x) = 3x - 6\), \(g(x) = 3 - x\) 2) \(f(x) = \frac{x}{x - 2}\), \(g(x) = x^3 + 1\) Evaluate the indicated function for \(f(x) = x^2 - 2\) and \(g(x) = x - 1\) algebraically. 3) \((f - g)(2)\) 4) \(\left(\frac{f}{g}\right)(t - 2)\) Find (a) \((f \circ g)(x)\) and (b) \((g \circ f)(x)\) 5) \(f(x) = x^4 - 4\), \(g(x) = \sqrt[4]{x + 4}\) 6) \(f(x) = x^2 + 9\), \(g(x) = \sqrt{x}\) Use the graphs of \(f\) and \(g\) to evaluate the functions: 7) (a) \((f \circ g)(1)\) (b) \((f \circ g)(4)\) 8) (a) \((f \circ g)(1)\) (b) \((g \circ f)(3)\) **Graphs Description:** - **Graph of \(f(x)\):** - The graph shows a V-shaped curve resembling an absolute value function. - It consists of points \((1, 2)\), \((2, 0)\), \((3, 2)\), and \((4, 3)\). - **Graph of \(g(x)\):** - The graph illustrates a downward-sloping linear function. - It includes points \((1, 3)\), \((2, 2)\), \((3, 1)\), and \((4, 0)\). Both graphs use a standard
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