Cryptography;perfect secracy

Problem 1: For an encryption scheme, let the key space and message space be the set of x-bit strings, and consider the encryption scheme defined by choosing a random key and setting Enck(m) = k||m (where || denotes concatenation, i.e., 0101||1111=01011111). In this encryption, the size of the key space equals the size of the message space, and the key is chosen uniformly from the key space. Is this encryption perfectly secret? (Explain your answer)