Does the graph represent a function that has an inverse function? Choose the correct answer below. No Yes
Does the graph represent a function that has an inverse function? Choose the correct answer below. No Yes
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Chapter 1 homework

Transcribed Image Text:### Inverse Functions
#### Question:
Does the graph represent a function that has an inverse function?
#### Graph Analysis:
The graph shown is a curve that appears to be the sum of a cubic polynomial function, crossing the x-axis at three points and the y-axis at one point.
- **Axes:** The graph includes both the x and y axes.
- **Curve:** The function depicted in the graph is not one-to-one. It crosses the y-axis at multiple points, indicating that there are multiple x-values for a single y-value.
#### Answer Choices:
- No
- Yes
#### Explanation:
A function has an inverse if it is one-to-one (bijective). That means every y-value should correspond to only one x-value. Since the given graph intersects the horizontal line (y-value) more than once for certain parts of the function, it fails the Horizontal Line Test and hence, the function does not have an inverse.
Please select the correct answer below based on this analysis:
O No
O Yes
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