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Chapter 2: Problem 72

Determine whether each function is even, odd, or neither. $$f(x)=x^{2} \sqrt{1-x^{2}}$$

Short Answer

Expert verified
The function \(f(x) = x^{2} \sqrt{1 - x^{2}}\) is an even function.

Step by step solution

01

Substitute x with -x in the function

First, substitute \(x\) with \(-x\) in the function \(f(x) = x^{2}\sqrt{1 - x^{2}}\), we get \(f(-x) = (-x)^{2}\sqrt{1 - (-x)^{2}}\). By simplifying, we get \(f(-x) = x^{2}\sqrt{1 - x^{2}}\).
02

Compare f(-x) and f(x)

Now, it's time to compare \(f(-x) = x^{2}\sqrt{1 - x^{2}}\) and \(f(x) = x^{2}\sqrt{1 - x^{2}}\). As they are both identical, we can conclude that f(x) is an even function.

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