Domain & Range Calculator
Enter a function of x. The calculator walks the expression to collect domain restrictions — zeros of any denominator, sign constraints inside square roots and logarithms — and reports the resulting set. The range is given for the common patterns (polynomial, sqrt, exp, ln, sin/cos) and reported as 'not determined' for trickier cases.
Frequently asked questions
What restrictions are detected?
Denominators are required not to vanish (excluding their real roots), square-root arguments must be ≥ 0, and logarithm arguments must be > 0. Inverse sine and cosine arguments are constrained to [−1, 1].
Why might the range say 'not determined'?
The range of an arbitrary function is genuinely hard to characterise. The calculator reports a closed form only for the standard patterns (polynomial, sqrt, exp, ln, sin/cos, atan).
How precise are the boundary values?
Boundary points come from polynomial roots up to degree 2; for higher-degree restrictions the calculator reports the symbolic inequality rather than numeric roots.