- #1
alman9898
- 10
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Homework Statement
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
Homework 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
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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