I'm doing a review for my discrete math test on functions and I'm having troubles with a few questions. Can I get some guidance in how to do these questions so I can be more prepared for the test?

1. (b) Show that the 'rule' $g:{Z}_{6}\to {Z}_{9}$ defined by $f([a{]}_{6})=[4a{]}_{9}$ is not a well-defined function.

2. Define a function $f:N\times N\to N$ by $f((a,b))=gcd(a,b)$

(a) show that f is not one-to-one

(b) show that f is onto

3. Let A, B, C be non-empty sets and let $f:A\to B$ and $g:B\to C$ be functions.

(a) Show that it $g\circ f$ is onto, then g is onto

(b) Find an example of functions f and g such that $g\circ f$ is onto but where f is not onto

1. (b) Show that the 'rule' $g:{Z}_{6}\to {Z}_{9}$ defined by $f([a{]}_{6})=[4a{]}_{9}$ is not a well-defined function.

2. Define a function $f:N\times N\to N$ by $f((a,b))=gcd(a,b)$

(a) show that f is not one-to-one

(b) show that f is onto

3. Let A, B, C be non-empty sets and let $f:A\to B$ and $g:B\to C$ be functions.

(a) Show that it $g\circ f$ is onto, then g is onto

(b) Find an example of functions f and g such that $g\circ f$ is onto but where f is not onto