f: Z -> Z defined by f(x) = x/2 if x is even, (x-1)/2 if x is odd.(adsbygoogle = window.adsbygoogle || []).push({});

Proof: If x is even:

x_{1}= 2k_{1}

x_{2}= 2k_{2}

Suppose f(x_{1}) = f(x_{2}), then

2k_{1}/2 = 2k_{2}/2

k_{1}= k_{2}

So if x is even, the function is one to one? Is this an okay proof for the first half of if x is even, then I just do the same for if x is odd correct?

Not sure if you can use a function to define the independent variable to prove if it's one-to-one or not.

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# Proving piece-wise function is one-to-one?

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