domain

The domain is the list of every input the function is allowed to accept — the menu of legal things you can feed the machine. If you try to feed it something off the menu, the machine simply has no answer to give.

Formally, the domain of a function f: A → B is the set A of all inputs for which f is defined. Two situations shrink a domain. First, the rule itself may forbid certain inputs: you cannot divide by zero, and you cannot take the square root of a negative number if you want a real answer. Second, the context may forbid them: if x counts people, negative or fractional values make no sense.

To find a domain from a formula, ask what would break. For 1/(x - 2), the value x = 2 makes the denominator zero, so the domain is all real numbers except 2. For sqrt(x), only x ≥ 0 keeps the result real, so the domain is x ≥ 0.