---
tag: 093CM69AGS
kind: definition
name: Domain
msc: ["03E20"]
defines: 0Q4CBD3HX0
uses: [0XHDTE5YMZ]
sources:
  - url: https://en.wikipedia.org/wiki/Domain_of_a_function
    locator: lead section
---

## Definition

Let $f \colon A \to B$ be a [[function|0XHDTE5YMZ]].
The domain of $f$ is the set $A$.

## Remarks

The function $f$ has a value $f(a)$ for each $a$ in its domain.
In calculus, the natural domain of a formula is the largest set of real numbers where the formula has a meaning. For $1/x$, it is $\mathbb{R} \setminus \{0\}$.

## Explanations

### L1 human

The domain says which inputs are allowed.
For the square root as a real function, the domain is the set of real numbers $x \ge 0$.