Statement : If  is even function, then  is exists.

If  is an even function, then .

Consider the even function .

Horizontal line test :

Observe the graph :

The function is not one-to-one since there is a horizontal line that intersects the graph more than once.

Therefore, an even function cannot be one-to-one function and hence inverse function cannot exist.

The statement is false.

The statement is false.