Domain

Definition

Let $f \colon A \to B$ be a function. 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 $x \ge 0$.