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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Question

Transcribed Image Text:**Problem Statement:**
Given two functions:
- \( f(x) = x^2 + x + 2 \)
- \( g(x) = x - 5 \)
Find the following:
(a) \( f + g \)
(b) \( f - g \)
(c) \( f \circ g \)
(d) \( g \circ f \)
(e) \( f(g(4)) \)
(f) \( g(f(4)) \)
(g) \( g \circ g \circ g \)
**Solutions:**
- **(a) \( f + g \):** Add the functions: \( f(x) + g(x) = (x^2 + x + 2) + (x - 5) \)
- **(b) \( f - g \):** Subtract the functions: \( f(x) - g(x) = (x^2 + x + 2) - (x - 5) \)
- **(c) \( f \circ g \):** Composition: \( f(g(x)) = f(x - 5) \)
- **(d) \( g \circ f \):** Composition: \( g(f(x)) = g(x^2 + x + 2) \)
- **(e) \( f(g(4)) \):** Evaluate: First find \( g(4) \), then evaluate \( f \)
- **(f) \( g(f(4)) \):** Evaluate: First find \( f(4) \), then evaluate \( g \)
- **(g) \( g \circ g \circ g \):** Apply \( g \) three times: \( g(g(g(x))) \)
Each box should contain the solution to its corresponding part.
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