Are the theorems g•f injective/surjective then f/g is injective/surjective invertible?

Question

i have questions.

I know that:

if $g \circ f$ is surjective than g is surjective;

If $g \circ f$ is injective than f is injective;

If g and f are both injective than $g \circ f$ is injective;

If g and f are both surjective than $g \circ f$ is surjective;

My questions are:

1. if g is surjective is $g \circ f$ surgective? I know it is not but i would like to see a proof and a counterexample

2. if f is injective is $g \circ f$ injective? Same as above

3. if g is surjective and f is injective is $g \circ f$ biijective?

Thanks