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Chapter 2: Problem 105

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 determine if a function is even, odd, or neither, you would need to replace \(x\) with \(-x\) in the function and simplify. If the resulting function is identical to the original function, it is an even function. If the resulting function is the negative of the original function, the function is odd. If neither of these conditions is met, the function is neither even nor odd.

Step by step solution

01

Determine if the function is 'even'

Replace \(x\) in the function with \(-x\) and simplify the equation. If the resulting function is identical to the original function (\(f(-x)=f(x)\)), then the function is 'even'.
02

Determine if the function is 'odd'

If the function is not 'even', replace \(x\) in the function with \(-x\) and simplify the equation again. If the resulting function is the negative of the original function (\(f(-x) = -f(x)\)), then the function is 'odd'.
03

Determine if the function is 'neither'

If none of the above conditions are satisfied, that is, the function is not identical to the original function nor is it the negative of the original function when \(x\) is replaced with \(-x\), then the function is 'neither'.

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