The table shows men's shoe sizes in the United States and the corresponding European shoe sizes. Let y = f(x) represent the function that gives the men's European shoe size in terms of x, the men's U.S. size. Men's U.S. shoe size Men's European shoe size 8 41 9 42 10 43 11 44 12 45 13 46 (a) Is f one-to-one? Explain. Yes, because no two elements in the domain correspond to the same element in the range.Yes, because two or more elements in the domain correspond to the same element in the range. No, because no two elements in the domain correspond to the same element in the range.No, because two or more elements in the domain correspond to the same element in the range. (b) Find f(13). (c) Find f −1(42), if possible. (If an answer does not exist, enter DNE.) (d) Find f(f −1(45)). (e) Find f −1(f(11)).
The table shows men's shoe sizes in the United States and the corresponding European shoe sizes. Let y = f(x) represent the function that gives the men's European shoe size in terms of x, the men's U.S. size. Men's U.S. shoe size Men's European shoe size 8 41 9 42 10 43 11 44 12 45 13 46 (a) Is f one-to-one? Explain. Yes, because no two elements in the domain correspond to the same element in the range.Yes, because two or more elements in the domain correspond to the same element in the range. No, because no two elements in the domain correspond to the same element in the range.No, because two or more elements in the domain correspond to the same element in the range. (b) Find f(13). (c) Find f −1(42), if possible. (If an answer does not exist, enter DNE.) (d) Find f(f −1(45)). (e) Find f −1(f(11)).
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
The table shows men's shoe sizes in the United States and the corresponding European shoe sizes. Let
y = f(x)
represent the function that gives the men's European shoe size in terms of x, the men's U.S. size.
| Men's U.S. shoe size |
Men's European shoe size |
|---|---|
| 8 | 41 |
| 9 | 42 |
| 10 | 43 |
| 11 | 44 |
| 12 | 45 |
| 13 | 46 |
(a) Is f one-to-one? Explain.
(b) Find f(13).
(c) Find f −1(42), if possible. (If an answer does not exist, enter DNE.)
(d) Find f(f −1(45)).
(e) Find f −1(f(11)).
Yes, because no two elements in the domain correspond to the same element in the range.Yes, because two or more elements in the domain correspond to the same element in the range. No, because no two elements in the domain correspond to the same element in the range.No, because two or more elements in the domain correspond to the same element in the range.
(b) Find f(13).
(c) Find f −1(42), if possible. (If an answer does not exist, enter DNE.)
(d) Find f(f −1(45)).
(e) Find f −1(f(11)).
Expert Solution
Step 1
The given data,
| Men's U.S shoe size | Men's European shoe size |
|
8 9 10 11 12 13 |
41 42 43 44 45 46 |
We have to find the given values.
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