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Chapter 1: Problem 122

If you are given a function's equation, how do you determine if the function is even, odd, or neither?

Short Answer

Expert verified
To check if a function \(f(x)\) is even, odd or neither, replace \(x\) by \(-x\) in the function and simplify. If \(f(-x) = f(x)\) then the function is even, if \(f(-x) = -f(x)\) the function is odd. If neither conditions is true then the function is neither even nor odd.

Step by step solution

01

Determine the Function Type

Evaluate \(f(-x)\) by replacing every instance of \(x\) in the function with \(-x\). Once evaluated, this will give three potential results. If \(f(-x) = f(x)\), then the function is even. If \(f(-x) = -f(x)\), then it's odd. If neither of these conditions is met, then the function is neither even nor odd.

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