What definitions and theorems you have to work with. That we don’t know.
In most developments of this material, one would normally have already have proven that Any subset of a countable set is a countable set. Having done that what is the point of this problem?
If and is uncountable there can be no injection .
For if there were its restriction to would be an injection.
I hope you can see how different many different approaches there are and see that the one you need to use depends on what you have already done.