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Math Help - functions Discrete math

  1. #1
    Member
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    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
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  2. #2
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    Is it not true that f(-2)=f(2)?
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