I have no idea where to even start on this proof. Any help would be greatly appreciated I think one of the problems I am having is that I don't quite understand the concept of an image. I know that, to show it is injective, I will have to show that h(x) = h(y) but I don't know how to start...

(I apologize if this is difficult to read)

Let h: X --> Y be a function. Show that h is injective iff im(h)(A intersect B) = im(h)(A) intersect im(h)(B) for all A,B subsets of X.

**** im(h)(A) means the image of h.... written as an h with a sub-star. Not sure if the notation I typed is correct.