Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question

Is it possible to help me for this exercise and write the steps? In the final answer, draw a circle around it so that I can understand and solve questions like this.

**Problem Statement:** Find \( f(g(x)) \) and \( g(f(x)) \) and determine whether the pair of functions \( f \) and \( g \) are inverses of each other. Given: \[ f(x) = \frac{4}{x - 3} \] \[ g(x) = \frac{4}{x} + 3 \] **Tasks:** a. Calculate \( f(g(x)) = \, \Box \) --- **Explanation:** To solve the problem, perform the following steps: 1. **Substitute** the function \( g(x) \) into \( f(x) \) to find \( f(g(x)) \). 2. **Substitute** the function \( f(x) \) into \( g(x) \) to find \( g(f(x)) \). 3. Compare whether \( f(g(x)) = x \) and \( g(f(x)) = x \). If both conditions hold true, the functions \( f \) and \( g \) are inverses of each other. This problem involves function composition and identifying properties of inverse functions, which is a fundamental concept in algebra and calculus.
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Transcribed Image Text:**Problem Statement:** Find \( f(g(x)) \) and \( g(f(x)) \) and determine whether the pair of functions \( f \) and \( g \) are inverses of each other. Given: \[ f(x) = \frac{4}{x - 3} \] \[ g(x) = \frac{4}{x} + 3 \] **Tasks:** a. Calculate \( f(g(x)) = \, \Box \) --- **Explanation:** To solve the problem, perform the following steps: 1. **Substitute** the function \( g(x) \) into \( f(x) \) to find \( f(g(x)) \). 2. **Substitute** the function \( f(x) \) into \( g(x) \) to find \( g(f(x)) \). 3. Compare whether \( f(g(x)) = x \) and \( g(f(x)) = x \). If both conditions hold true, the functions \( f \) and \( g \) are inverses of each other. This problem involves function composition and identifying properties of inverse functions, which is a fundamental concept in algebra and calculus.
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