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Chapter 2: Problem 61

Determine whether each function is even, odd, or neither. $$f(x)=x^{3}+x$$

Short Answer

Expert verified
The function \(f(x)=x^{3}+x\) is odd.

Step by step solution

01

Calculate \(f(-x)\)

Plug \(-x\) into the function \(f(x) = x^{3} + x\), then \(f(-x) = (-x)^{3} + (-x) = -x^{3} - x\).
02

Compare \(f(-x)\) with \(f(x)\) and \(-f(x)\)

Now compare \(f(-x)\) with \(f(x)\) and \(-f(x)\). If \(f(-x) = f(x)\), then the function is even. If \(f(-x) = -f(x)\), then the function is odd. Here we see that, \(f(-x)= -f(x)\), so function is odd.

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