What the app does
Every operation that can fail imposes a condition: a denominator must not be zero, an even root needs a non-negative argument, a logarithm a strictly positive one, and arcsine and arccosine need an argument between −1 and 1. Those conditions are read straight off the expression, then the real line is cut at every candidate boundary and the pieces where all of them hold are kept.
Why it matters
The domain is the stage on which everything else happens. Every later step — signs, limits, derivatives, the plot — is restricted to it, and a point outside it can never be a solution no matter how good it looks.
Read further
- Domain of a function Wikipedia
- Domain Wolfram MathWorld
- Continuity Paul's Online Notes