I have a Linear Algebra exam coming up (i'm clueless, and i just want to pass). I have the previous exam but there are no solutions. Anyone knows how should i solve this, or can give me a link to some Linear Algebra problems that have exercises like this?.

Trying to translate as best as i can from my native language:

Find one base in Ker(f) and Im(f), where f:R^2 -> R^2
f(x, y) = (x, 2x)

This is NOT a homework