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1. Suppose: f(x) = 2x + 5, g(x) = - x². a. Find g 8(S(x)) 'b. Is g(f(x)) one to one? Justify your answer.

1. Suppose: f(x) = 2x + 5, g(x) = - x². a. Find g 8(S(x)) 'b. Is g(f(x)) one to one? Justify your answer.

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 1 Suppose: \( f(x) = 2x + 5 \), \( g(x) = -x^2 \). #### a. Find \( g(f(x)) \). #### b. Is \( g(f(x)) \) one-to-one? Justify your answer. --- **Explanation:** This problem involves function composition and determining whether a function is one-to-one. 1. **Function Composition:** - We are given two functions, \( f(x) \) and \( g(x) \). - \( f(x) = 2x + 5 \) is a linear function. - \( g(x) = -x^2 \) is a quadratic function. - To find \( g(f(x)) \), substitute \( f(x) \) into \( g(x) \). 2. **One-to-One Function:** - A function is one-to-one if each element of the range is mapped by exactly one element of the domain. - This often involves checking whether the function is strictly increasing or decreasing.
Transcribed Image Text:### Problem 1 Suppose: \( f(x) = 2x + 5 \), \( g(x) = -x^2 \). #### a. Find \( g(f(x)) \). #### b. Is \( g(f(x)) \) one-to-one? Justify your answer. --- **Explanation:** This problem involves function composition and determining whether a function is one-to-one. 1. **Function Composition:** - We are given two functions, \( f(x) \) and \( g(x) \). - \( f(x) = 2x + 5 \) is a linear function. - \( g(x) = -x^2 \) is a quadratic function. - To find \( g(f(x)) \), substitute \( f(x) \) into \( g(x) \). 2. **One-to-One Function:** - A function is one-to-one if each element of the range is mapped by exactly one element of the domain. - This often involves checking whether the function is strictly increasing or decreasing.
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