My text book says the domain and co-domain need to be either $\mathbb{R}$ or some subset of $\mathbb{R}$ but sometimes I read on the internet, a function that gives real values is a real valued function.
I'm not sure which one's correct though, can anyone help me out here?
For instance, would you say
$$ f \, : \mathbb{C} \to \mathbb{R}$$ is a real valued function even though the domain is a set of complex numbers?
Best Answer
If $X$ is an arbitrary set, we call a function $f$ defined on $X$ real-valued so long as it maps $X$ into some subset (possibly the entirety of) the real numbers $\mathbb{R}$.