# Thread: Need Help!!! Dealing with Domain and Codomain

1. ## 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?

2. 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.

### give an example of increasing function with the set of real numbers as its domain and codomain that is not one to one

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