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 $\"\"$ , the function is an odd function.

Yes, there is a function both even and odd.

The function $\"\"$ is both even and odd function.