Domain & Range Calculator (Square Root / Rational)
Domain restrictions for sqrt and rational expressions.
Enter your values
Choose one of: sqrt(mx+b), 1/(mx+b).
Enter the m you are working with.
Enter the b you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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.
At a glance
| What it does | Domain restrictions for sqrt and rational expressions. |
|---|---|
| Category | Math |
| Inputs needed | Expression type, m, b |
| Main output | Domain |
| Formula | sqrt(mx+b): domain x >= -b/m. 1/(mx+b): domain x != -b/m. |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Expression type
- Choose one of: sqrt(mx+b), 1/(mx+b).
- m
- Enter the m you are working with.
- b
- Enter the b you are working with.
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.
What do I need to enter into the Domain & Range Calculator (Square Root / Rational)?
Just 3 values: expression type, m, b. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Domain & Range Calculator (Square Root / Rational) work out the answer?
Square roots require the radicand to be >= 0; rational expressions exclude values that make the denominator zero. It applies the formula sqrt(mx+b): domain x >= -b/m. 1/(mx+b): domain x != -b/m. and shows the working so you can check each step by hand.
Is the Domain & Range Calculator (Square Root / Rational) free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.