A function is said to be an even function if the sign of the image does not change when the sign of the preimage changes.
Conversely, a function is called an odd function when the sign of the image changes when the sign of the preimage changes.
For Even functions, f(x) = f(-x).
For the Odd function, f(x) = -f(-x).
| Examples of Even Function: f(x) = x2 . We have f(1) = 1 and f(-1) = 1 hence f(1) = f(-1). This is true fora ∀ x ∈ R. Another example would be mod function |x|. |
| Examples of Odd Function: f(x) = x3 . We have f(1) = 1 and f(-1) = -1 hence f(1) = -f(-1). This is true for ∀ x ∈ R. |
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