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Chapter 1: Problem 57

Determine whether the function has an inverse function. If it does, then find the inverse function. $$f(x)=x^{4}$$

Short Answer

Expert verified
The function \(f(x) = x^4\) does not have an inverse function.

Step by step solution

01

Identify the Function

The function given is \(f(x) = x^4\).
02

Apply the Horizontal Line Test

The horizontal line test can be used to determine whether a function has an inverse. For the function \(f(x) = x^4\), all horizontal lines would intersect the graph at more than one point, meaning the function does not pass the horizontal line test.
03

Conclude on the Presence of an Inverse

As the function \(f(x) = x^4\) does not pass the horizontal line test, it does not have an inverse function. So, we do not need to proceed to find the inverse.

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