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I am given the simple relation $f(x)=\sqrt{x}$, where $f$ maps $R \rightarrow R$, and I am suppose to determine whether or not it is a function.
I figured that it was a function, because in the definition of a function it doesn't mention anything about not being defined at a value. Clearly, this function isn't onto though, because any value in the codomain that is less than $0$ won't be assigned to a domain value.
1 Answer
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A function must be defined on it's entire domain. This is false here, so $f:R \to R$ is not a function.
However if the domain was $R_{ \ge0}=[0,\infty)$, $f$ would have been a function.
