Proof if Function is Injective or Surjective.

[RatherBadAtMath]

Hi everyone I am having trouble with prooving whether or not this function is injective, surjective or bijective as prior to this I have always been provided with a set of values.

Any help would be greatly appreciated.

 

[yoscar04]

Hi, what have you tried so far? Start with the definitions of injective, surjective and bijective functions and tell us where you got stuck.

 

[Steven G]

Is f 1-1? Suppose f(a, b) = f(c, d). Must (a, b) = (c, d)? If yes, then f is 1-1. If no, then f is not 1-1.

Is f surjective? Pick some element in Q, say a/b. Is there a (p,q) such that f(p,q) = a/b. If yes, then f is surjective. If not then f is not surjective.

Is f a bijection? What is the definition of a bijection?

 

[HallsofIvy]

You will need to consider the fact that \(\displaystyle \frac{1}{2}= \frac{2}{4}\).