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g(x) h(x) F(x) G(x) 4 7 9 6 4 2 387826 5 4 5 6 7 3 12 748 7 Which of these functions is one-to-one? 1. F(x) 2. f(x) 3. g(x) 4. h(x) 5. G(r)

g(x) h(x) F(x) G(x) 4 7 9 6 4 2 387826 5 4 5 6 7 3 12 748 7 Which of these functions is one-to-one? 1. F(x) 2. f(x) 3. g(x) 4. h(x) 5. G(r)

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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### Five Functions Defined by the Table The table below displays values for five different functions, \(f(x)\), \(g(x)\), \(h(x)\), \(F(x)\), and \(G(x)\), each defined over the domain \(x = 1, 2, 3, 4, 5, 6\). | \(x\) | 1 | 2 | 3 | 4 | 5 | 6 | |--------|---|---|---|---|---|---| | \(f(x)\) | 7 | 5 | 1 | 6 | 4 | 2 | | \(g(x)\) | 4 | 7 | 9 | 6 | 4 | 2 | | \(h(x)\) | 3 | 8 | 7 | 2 | 7 | 6 | | \(F(x)\) | 5 | 5 | 4 | 5 | 6 | 7 | | \(G(x)\) | 1 | 2 | 7 | 4 | 8 | 7 | ### Question: **Which of these functions is one-to-one?** 1. \(F(x)\) 2. \(f(x)\) 3. \(g(x)\) 4. \(h(x)\) 5. \(G(x)\) ### Explanation: A function is one-to-one if it assigns distinct outputs for distinct inputs, meaning no two different inputs \(x_1\) and \(x_2\) have the same output value. - **\(f(x)\)**: All values are unique. - **\(g(x)\)**: The value \(4\) repeats. - **\(h(x)\)**: The value \(7\) repeats. - **\(F(x)\)**: The value \(5\) repeats. - **\(G(x)\)**: The value \(7\) repeats. In this context, the only function that is one-to-one is **\(f(x)\)**.
Transcribed Image Text:### Five Functions Defined by the Table The table below displays values for five different functions, \(f(x)\), \(g(x)\), \(h(x)\), \(F(x)\), and \(G(x)\), each defined over the domain \(x = 1, 2, 3, 4, 5, 6\). | \(x\) | 1 | 2 | 3 | 4 | 5 | 6 | |--------|---|---|---|---|---|---| | \(f(x)\) | 7 | 5 | 1 | 6 | 4 | 2 | | \(g(x)\) | 4 | 7 | 9 | 6 | 4 | 2 | | \(h(x)\) | 3 | 8 | 7 | 2 | 7 | 6 | | \(F(x)\) | 5 | 5 | 4 | 5 | 6 | 7 | | \(G(x)\) | 1 | 2 | 7 | 4 | 8 | 7 | ### Question: **Which of these functions is one-to-one?** 1. \(F(x)\) 2. \(f(x)\) 3. \(g(x)\) 4. \(h(x)\) 5. \(G(x)\) ### Explanation: A function is one-to-one if it assigns distinct outputs for distinct inputs, meaning no two different inputs \(x_1\) and \(x_2\) have the same output value. - **\(f(x)\)**: All values are unique. - **\(g(x)\)**: The value \(4\) repeats. - **\(h(x)\)**: The value \(7\) repeats. - **\(F(x)\)**: The value \(5\) repeats. - **\(G(x)\)**: The value \(7\) repeats. In this context, the only function that is one-to-one is **\(f(x)\)**.
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