Prove that a function is not PRF?
For something to be a PRF, it must be impossible for a probabilistic polynomial time algorithm to distinguish it from a random function. The distinguisher you note in your attempt is correct, as a random function would not have that property (xor two calls with the same key but different x values and you get the xor of the two x values).

As a side note, these notes are very good when it comes to PRFs. Especially 3.3 and 3.4.