# functions Discrete math

• Sep 25th 2010, 02:09 PM
robasc
functions Discrete math
I am working on this problem:

determine whether the function f(n) = n^2-1 is one-to-one, onto, or both. Prove your answer. The domain and codomain of f(n) is the set of all integers. Show all work.

This is what I have done so far:

Code:

``` Assume that : f(a) = f(b), then a = b   translation:   a^2 - 1 = b^2-1  add one to both sides   a^2 = n^2        take the square root of both sides   a = b    therefore, f is one-to-one```
I am assuming that the function f(n) is not onto Y because f(n) does not equal Y.

but how do I prove this. In other words, how am I supposed to prove this, algebraically or a statement or does it matter?

Thanks
• Sep 25th 2010, 02:13 PM
Plato
Is it not true that $f(-2)=f(2)?$