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If f(x) = x2 + x + 2 and g(x) = x – 5, find the following. (а) f + g (b) f - g (c) fog (d) дof (e) f(g(4)) (f) g(f(4)) (g) gogog

If f(x) = x2 + x + 2 and g(x) = x – 5, find the following. (а) f + g (b) f - g (c) fog (d) дof (e) f(g(4)) (f) g(f(4)) (g) gogog

Calculus: Early Transcendentals
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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**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.
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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