Domain (Function)

algebra

Definition

Domain (Function)

The domain of a function $f:D\to C$ is the set $D$ of inputs on which $f$ is defined:

$$\mathrm{dom}(f)=D,\forall x\in D\exists !y\in C:f(x)=y.$$

The domain is part of the function’s specification. An object outside $D$ is not an admissible input, even if the same defining expression could be evaluated there.

Examples

Square root

For

$$f:[0,\infty )\to \mathbb{R},f(x)=\sqrt{x},$$

the domain is $\mathrm{dom}(f)=[0,\infty )$.