Hey, I don't know how to prove this.
So... help me
Let f: X -> Y and g: Y -> X be functions so that g o f = 1x(which means Identity function). Prove that f is injective and g is surjective. Need either be bijective?
On hints sheet, This has 3 parts. Justify your answer to last part w/ a proof or counterexample.
Can I prvoe g's being surjective by same way?
Suppose g is not surjective. Then there exists such that a is not contained in the image of set Y. By definition, g(a) doesn't exist. But in order for g to be a function, g(a) should be defined(not sure about this part).