Precalculus · Grades 10 to 12
Functions and domains
Find the inputs that a function allows.
The idea
A function pairs each input with exactly one output. Its domain is the set of inputs that give a real output.
Two numbers are forbidden: a denominator of zero and a square root of a negative number. Check for both when you find a domain.
Worked examples
- How to Find the Domain of a Function Find the domain of f(x) = 1/(x - 4). Three steps, the zero-denominator rule, the set-notation mistakes to avoid and practice problems.
- How to Find the Domain of a Square Root Function Find the domain of f(x) = sqrt(x - 7). Three steps that set the radicand not negative, and the inequality sign mistakes to avoid.
- How to Find the Domain of a Fraction Function Find the domain of f(x) = 1/(x + 5). Three steps that exclude the zero denominator, and the include-the-excluded-value mistakes.
Practice this topic
4 problems with answers.