What the Domain Is

The domain of a function is the set of inputs it accepts. For a rule like 2x + 5, every real number works, so the domain is all real numbers.

Some rules refuse certain inputs. $f\left(x\right) = \frac{1}{x}$ has no output at 0, because dividing by zero is undefined. $g\left(x\right) = \sqrt{x}$ has no real output for a negative input, because no real number squares to a negative. Those inputs are outside the domain.

So finding a domain is a hunt for trouble: look for a division that could hit zero and a square root that could see a negative. For the rules in this section, everything else is allowed.