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Chapter 2: Problem 79

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=\frac{x^{4}}{4} $$

Short Answer

Expert verified
The function given \(f(x)=\frac{x^{4}}{4}\) is not one-to-one as it fails the horizontal line test. Therefore, it does not have an inverse that is a function.

Step by step solution

01

Graph the function

Graph the function \(f(x) = \frac{x^{4}}{4}\). This will help visualize the function's behavior.
02

Apply the horizontal line test

Draw horizontal lines across the graph of the function. If any line touches the graph at more than one point, the function is not one-to-one.
03

Analyze the result

If the function passes the horizontal line test, it is one-to-one, and it has an inverse that is a function. If it fails the horizontal line test, it is not one-to-one, and it does not have an inverse that is a function.

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