Yes, there is a function both even and odd.

The function is both even and odd function.

If is an even function, then .

If is an odd function, then .

The zero function is .

Substitute in .

Since , the function is an even function.

Multiply each side by negative one.

           [ Since ]

Since , the function is an odd function.

Yes, there is a function both even and odd.

The function is both even and odd function.