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Chapter 2: Problem 28

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

Short Answer

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

Step by step solution

01

Evaluate the function at -x

The first step in solving this problem is to replace x in the function with -x. Therefore, substitute -x into the function \(f(x)=x\sqrt{1-x^{2}}\) to get \(f(-x) = -x\sqrt{1-(-x)^{2}}\).
02

Simplify the function at -x

By simplifying the function at -x, we get \(f(-x) = -x\sqrt{1-x^{2}}\). The squared part of the function takes away the negative sign and leaves the function unchanged.
03

Evaluate if the function is even, odd, or neither

We can see that \(f(-x) = -f(x)\), indicating that for every x in the domain of f, f(-x) is equal to -f(x). Hence the function f(x) is an odd function.

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Most popular questions from this chapter

How is the standard form of a circle's equation obtained from its general form?

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