Prove that an infinite set is semidecidible

Question

I have been asked to prove that:

Being C an infinite set. Prove that C is semidecidable if and only if exists a total computable function that is injective and whose image is C.

I've read the wikipedia articles of computable function and recursively enumerable set and I saw these properties are true. But I have no idea how to start the proof.

Could you please help me?

Thanks in advance.