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Math Help - Need Help!!! Dealing with Domain and Codomain

  1. #1
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    Need Help!!! Dealing with Domain and Codomain

    I have no idea how to do this?

    Q: Give an example of an increasing function with the set of all real numbers as its domain and codomain that is not one-to-one?
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  2. #2
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    I think one simple example would be the function f:R \rightarrow R defined by f(x)=x^2. This function is increasing on R^+, and clearly is not one-to-one since you can have f(a)=f(-a)=a^2 where a \in R, contradicts the definition of being one-to-one.
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