(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine whether f: ZxZ->Z is onto if

(a) f(m, n) = 2m-n

(b) f(m, n) = n^2 - m^2

(c) f(m, n) = m + n + 1

(d) f(m, n) = |m| - |n|

(e) f(m, n) = m^2 - 4

2. Relevant equations

A function is onto if for every y in the codomain there is at least one X in the domain st f(x) = y

3. The attempt at a solution

I have no idea how to start proving this. I know I'm supposed to prove that for every integer y, there is at least 1 (m, n) pair, but that requires solving for another variable m or n doesn't it? This leaves a lot of m,n to test for yes?

For example, I can go about the first one by setting m = (y+n)/2 and if y = 0 and n is odd then m is not an integer. However, I know from reading ahead that the first one is onto.

For the last one I can do

sqrt(y+4) = m

If y = 1, then m is not an integer and so y = 1 is not in the range

Am I supposed to prove the cases where m is odd, n is even, both are even, both are odd, m is even, n is odd?

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# Homework Help: Proving something is onto

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