Finding the domain by investigating continuity (KristaKingMath)
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In order to find the domain of a function, you have to be able to say where a function is continuous and discontinuous. A function will be continuous wherever it isn’t discontinuous, so to figure out where the function is continuous, we just need to find all the points of discontinuity.
A function is discontinuous wherever it’s undefined, or wherever the one-sided limits (left- and right-hand limits) aren’t equal to each other. Functions will be undefined whenever a denominator is equal to 0, whenever the value inside a square root is negative, whenever the value inside a natural log is negative, etc.
Once we find all of the points at which the function is discontinuous, we can say that the function is continuous at all other points. Since the domain of the function is defined everywhere the function is continuous, we can say that the domain of the function is all of the points where the function is continuous.
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