Let K be a normal subgroup of a group G. Define a function f:G →G/K by f(x)=xK. Find the kernel Ker(f) and the image Im(f) = f(G) of f.
Please do go back to your notes/books, read carefully and slowly until you understand the basic definitions in basic group theory, then think a little, do some work AND THEN, if you're still stuck somewhere, write back and ask for others to help you out to do your homework, and not all of it.
Tonio