Odd and Even Functions

If f(x) = f(−x) for all x in the domain then the function is called an even function.

If f(x) = − f(−x) for all x in the domain then the function is called an odd function.

There are many functions which are neither even nor odd. For even function, y axis divides the graph of the function into two exact pieces (symmetric). The graph of an even function is symmetric about y-axis. The graph of an odd function is symmetrical about origin.

Properties

1. Sum of two odd functions is an odd function.

2. Sum of two even functions is an even function.

3. Sum of an odd and an even function is neither even nor odd.

4. Product of two odd functions is an even function.

5. Product of two even functions is an even function.

6. Product of an odd and an even function is an odd function.

7. Quotient of two even functions is an even function.

8. Quotient of two odd functions is an even function. 

9. Quotient of a even and an odd function is an odd function.