For any given equation of a function how do you determine if

For any given equation of a function, how do you determine if the function is even, odd, or neither?

Solution

To determine whether a function is even or odd, we substitute –x in for x, and then simplify. If we end up with exactly the same function that we started with (that is, if f(–x) = f(x) or if f (x ) – f (-x) = 0 ) then the function is even. If we end up with the exact opposite of what we started with (that is, if f(–x) = –f(x), or f(-x) + f (x) = 0), then the function is odd. In all other cases, the function is \"neither even nor odd\".

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