Definition:Real-Valued Function

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Definition

Let $f: S \to T$ be a function.

Let $S_1 \subseteq S$ such that $f \left({S_1}\right) \subseteq \R$.


Then $f$ is said to be real-valued on $S_1$.


That is, $f$ is defined as real-valued on $S_1$ if and only if the image of $S_1$ under $f$ lies entirely within the set of real numbers $\R$.


A real-valued function is a function $f: S \to \R$ whose codomain is the set of real numbers $\R$.

That is, $f$ is real-valued if and only if it is real-valued over its entire domain.


Also see