Prooving surjective and injective functions

**neelpatel89** · October 20th 2009, 10:33 AM

Let g : A -> B and f : B -> C be functions.
Show that if f and g are injective, then f o g is injective.
Show that if f and g are surjective, then f o g is surjective.

i don't know how to proove it

**p00ndawg** · October 20th 2009, 01:45 PM

b.

since f is surjective, rng f = C. That is, for any c $\in$ C, there exists b $\in$ B such that f(b) = c. Now since g is surjective, there exists an a $\in$ A such that g(a) = b. but then (f o g)(a) = f(g(a)) = f(b) = c, so
f o g is surjective.

**redsoxfan325** · October 20th 2009, 01:51 PM

Originally Posted by neelpatel89

Let g : A -> B and f : B -> C be functions.
Show that if f and g are injective, then f o g is injective.
Show that if f and g are surjective, then f o g is surjective.

i don't know how to proove it