need help with question 37 and the function is also listed **Exercise 33–38****Objective:**Find the functions (a) \( f \circ g \), (b) \( g \circ f \), (c) \( f \circ f \), and (d) \( g \circ g \) and their domains. ## Problem 37Given the functions \( f(x) \) and \( g(x) \), where:\[ f(x) = x + \frac{1}{x} \]and\[ g(x) = \frac{x + 1}{x + 2} \]Explain the behavior, transformations, and any interesting properties of these functions. Use this example as a starting point for solving problems involving combinations of rational functions. ### Further AnalysisAnalyze the domain, range, asymptotes, and any critical points of the functions \( f(x) \) and \( g(x) \). Discuss how to find these characteristics step-by-step.

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Answered: 1 g(x) x + 1 37. f(x) = x + x + 2

Math

Calculus

1 g(x) x + 1 37. f(x) = x + x + 2

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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