College Algebra / Unit 5 Alg 252 worked example, 60 to 90 seconds
Finding a Domain from an Equation
The idea
Finding a domain from an equation means excluding what breaks the rule — zero denominators out, negative radicands out under even roots — and writing the survivors in interval notation.
In practice
Find the domain of f(x) = 1/(x − 3). One hazard: the denominator zeroes at x = 3. Domain: (−∞, 3) ∪ (3, ∞). Now g(x) = √(x − 2). One hazard: an even root refuses negatives, so x − 2 ≥ 0, meaning x ≥ 2. Domain: [2, ∞) — bracket at 2, because zero under the radical is legal. A rule with both hazards runs both hunts and keeps the intersection. Most formulas have no hazards at all; their domain is every real number, written (−∞, ∞).
Where people slip
The bracket-versus-parenthesis call at each boundary is part of the answer.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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