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The domain of a function is the complete set of input values (x) for which the function is defined and produces a real output. The range is the complete set of output values (y). Identifying domain and range restrictions is a fundamental skill in algebra and calculus — it determines where functions are valid and where operations such as integration or root-finding apply.

공식

1/expression: domain excludes values where expression = 0

단계별 가이드

1√(expression): domain requires expression ≥ 0
2ln(expression): domain requires expression > 0 (strictly positive)
31/expression: domain excludes values where expression = 0
4Linear ax+b: domain is all real numbers (−∞, +∞)
5Composite functions: apply restrictions at each step

풀어진 예시

입력

f(x) = √(x−3)

결과

Domain: x ≥ 3; Range: y ≥ 0

x−3 must be non-negative

입력

f(x) = ln(2x+4)

결과

Domain: x > −2; Range: all reals

2x+4 > 0 → x > −2

입력

f(x) = 1/(x²−4)

결과

Domain: x ≠ ±2; Range: y ≠ 0

Denominator cannot be zero

자주 묻는 질문

What is Function Domain?

The domain of a function is the complete set of input values (x) for which the function is defined and produces a real output. The range is the complete set of output values (y)

How accurate is the Function Domain calculator?

The calculator uses the standard published formula for function domain. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Function Domain calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Function Domain calculator use?

The core formula is: 1/expression: domain excludes values where expression = 0. Each step in the calculation is shown so you can verify the result manually.

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