Domain & Range Calculator (Square Root / Rational)
Domain restrictions for sqrt and rational expressions.
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ⓘ Live results
Results
- Domain
- x >= 4
- Range
- y >= 0
- Boundary point
- 4
Quick answer
Square roots require the radicand to be >= 0; rational expressions exclude values that make the denominator zero.
sqrt(mx+b): domain x >= -b/m. 1/(mx+b): domain x != -b/m.
How to use the Domain & Range Calculator (Square Root / Rational)
- 1Choose whether your expression is a square root or a simple rational function.
- 2Enter the linear coefficients m and b inside the expression.
- 3Read the domain restriction and typical range.
Worked example
Using the values the calculator loads with:
Inputs
- Expression typesqrt(mx+b)
- m1
- b-4
Results
- Domainx >= 4
- Rangey >= 0
- Boundary point4
Frequently asked questions
Why does sqrt need a restriction?
Real square roots are undefined for negative radicands.
Why does 1/(mx+b) exclude a point?
Division by zero is undefined at that x value.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.