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Chapter 1: Problem 43

Use a graphing utility to graph the function, and use the Horizontal Line Test to determine whether the function has an inverse function. $$f(x)=-2 x \sqrt{16-x^{2}}$$

Short Answer

Expert verified
After graphing and applying the Horizontal Line Test, it will be deduced whether the function has an inverse or not. The answer depends on the outcome of the Horizontal Line Test.

Step by step solution

01

Graph the function

Using a graphing tool, plot the function \( f(x) = -2x \sqrt{16-x^{2}} \). Make sure to have a sufficient range on both x-axis and y-axis to clearly see the function.
02

Apply the Horizontal Line Test

With the graph of the function, check if any horizontal line can intersect the function's graph more than once. If so, the function does not have an inverse. If no horizontal line intersects the graph more than once, the function has an inverse.
03

Conclude whether the function has an inverse

Based on the result of the Horizontal Line Test, conclude whether the function \( f(x) = -2x \sqrt{16-x^{2}} \) has an inverse or not.

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