Domain Error Calculator

A Domain Error Calculator helps identify and prevent errors that occur when a function’s input falls outside its valid domain. In mathematics, certain operations, such as square roots of negative numbers or division by zero, result in undefined values. This calculator ensures inputs remain within the function’s permissible range, avoiding computation errors.

Formula of Domain Error Calculator

For Square Root Functions: Domain Error in √x occurs when:

x < 0

Valid domain:

x ≥ 0

For Logarithmic Functions: Domain Error in log(x) occurs when:

x ≤ 0

Valid domain:

x > 0

For Tangent Function: Domain Error in tan(x) occurs when:

x = (π/2) + nπ, where n is any integer

Valid domain:

x ≠ (π/2) + nπ

For Inverse Sine and Cosine: Domain Error in arcsin(x) or arccos(x) occurs when:

|x| > 1

Valid domain:

-1 ≤ x ≤ 1

For Division: Domain Error in 1/x or expressions with x in the denominator occurs when:

x = 0

Valid domain:

x ≠ 0

For Even Roots: Domain Error in ⁿ√x (where n is even) occurs when:

x < 0

Valid domain:

x ≥ 0

Finding the Domain of a Function:

1. Identify all expressions that could cause domain errors.
2. Set up inequality constraints to avoid these errors.
3. Solve the system of inequalities to find the valid domain.

Example: Find the domain of f(x) = √(x-3)/(x²-4)

Step 1: Identify potential domain errors

• √(x-3) requires x-3 ≥ 0, therefore x ≥ 3.
• 1/(x²-4) requires x²-4 ≠ 0, therefore x ≠ ±2.

Step 2: Combine constraints

• Domain = {x | x ≥ 3 and x ≠ ±2}
• Since x ≥ 3, we know x ≠ -2 automatically.
• Final domain = {x | x ≥ 3 and x ≠ 2} = [3,2)∪(2,∞)

Commonly Searched Terms

Function Type	Domain Restriction
Square Root (√x)	x ≥ 0
Logarithm (log x)	x > 0
Tangent (tan x)	x ≠ (π/2) + nπ
Inverse Trig (arcsin x, arccos x)	-1 ≤ x ≤ 1
Rational (1/x)	x ≠ 0
Even Roots (ⁿ√x, n even)	x ≥ 0

Example of Domain Error Calculator

Find the domain of g(x) = log(x-5)/(x² – 9)

Step 1: Identify domain restrictions

• log(x-5) requires x-5 > 0 → x > 5.
• 1/(x² – 9) requires x² – 9 ≠ 0 → x ≠ ±3.

Step 2: Combine constraints

• x > 5 and x ≠ ±3.
• Since x > 5, the condition x ≠ -3 is automatically satisfied.
• Final domain: {x | x > 5 and x ≠ 3} = (5,3) ∪ (3,∞).

Most Common FAQs