Let $S \subseteq \R$.
Let $f: S \to \R$ be a real function.
It is frequently the case that $S$ is not explicitly specified. If this is so, then it is understood that the domain is to consist of all the values in $\R$ for which the function is defined.
This often needs to be determined as a separate exercise in itself, by investigating the nature of the function in question.
Also known as
- 1914: G.W. Caunt: Introduction to Infinitesimal Calculus ... (previous) ... (next): Chapter $\text I$: Functions and their Graphs: $2$. Functions
- 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations ... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $2 \text B$: The Meaning of the Term Function of One Independent Variable
- 1964: William K. Smith: Limits and Continuity ... (previous) ... (next): $\S 2.2$: Functions
- 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $\S 1.3$: Functions and mappings. Images and preimages
- 1968: Peter D. Robinson: Fourier and Laplace Transforms ... (next): $\S 1.1$. The Idea of an Integral Transform