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The 51 pages that link to Domain of a function, each with the reason it gives.

• FunctionRelated: A function assigns an output to every input in its domain.

• LogarithmRelated: For real logarithms, the input must be positive and the base must be positive but not 1.

• Boundary value problemRelated: Its boundary determines where boundary data are imposed.

• ContinuityRelated: Continuity is tested relative to the points and boundary of the function’s domain.

• Scalar fieldRelated: The domain supplies the points at which the field has values.

• BijectionRelated: Its elements are paired with codomain elements by a bijection.

• Function compositionRelated: An input must lie in the inner function’s domain, and its output must suit the outer function.

• Variable (mathematics)Related: A variable's permitted values are often restricted by a domain.

• Constraint satisfaction problemRelated: Each CSP variable draws its candidate values from a domain.

• Rational functionRelated: Denominator zeros determine which inputs must be excluded.

• Identity theoremRelated: The theorem applies on a connected open domain, not an arbitrary set.

• Injective functionRelated: Injectivity depends on which inputs the function is allowed to compare.

• Interval (mathematics)Related: Many real functions are defined on intervals, which shape their continuity and differentiability.

• CodomainRelated: The domain and codomain together specify the sets a function maps between.

• Conformal mapRelated: Conformal maps act between domains, and their shapes constrain possible mappings.

• Difference quotientRelated: Both sampled inputs must belong to the function’s domain.

• Maximum principleRelated: Interior and boundary extrema are defined relative to the equation’s domain.

• FunctorRelated: The source category supplies the objects and morphisms a functor maps.

• Surjective functionRelated: Surjectivity asks whether inputs from this set reach every codomain element.

• Image (mathematics)Related: Changing the selected inputs can change the image.

• Partial functionRelated: The partial function’s domain is the subset on which it has values.

• EquationRelated: A domain can restrict which candidate values are permitted in an equation.

• Periodic boundary conditionRelated: Periodic conditions apply at the edges of this set.

• Change of variablesRelated: A substitution changes the region of inputs over which the transformed problem is defined.

• Dirichlet boundary conditionRelated: Its boundary is where the specified function values are imposed.

• Bounded functionRelated: Changing the domain can turn an unbounded function into a bounded restriction.

• Piecewise functionRelated: The domain is divided into the regions where different rules apply.

• Dirichlet problemRelated: The differential equation is imposed inside this region.

• Equality conditionRelated: Equality cases must be drawn from inputs where every expression in the inequality exists.

• Trigonometric identityRelated: An identity must hold only where every expression in its equation is defined.

• Algebraic identityRelated: An identity holds only for values where its expressions are defined.

• Graph of a functionRelated: Each domain element contributes an input coordinate to the graph.

• Common logarithmRelated: The real-valued common logarithm has positive numbers as its domain.

• Left inverseRelated: The identity required by g∘f acts on f’s domain.

• One-sided limitRelated: A domain may permit approach from only one side near a boundary.

• Real-valued functionRelated: Its elements need not be real numbers, even when every output is.

• Zero of a functionRelated: Only domain elements can qualify as zeros, even if an equation has other formal solutions.

• Algebraic equationRelated: Restrictions on allowed variable values can exclude otherwise tempting solutions.

• Constant functionRelated: The fixed-output condition must hold for every element in this set.

• Logarithmic differentiationRelated: Real logarithms require positive inputs, so the method needs care when the function changes sign.

• Range of a functionRelated: Changing the allowed inputs can change which values the function attains.

• Even and odd functionsRelated: An even or odd function must have a domain closed under negation.

• Vector-valued functionRelated: The domain specifies which parameters or points receive vector outputs.

• Y-interceptRelated: If zero is excluded from the domain, the function has no y-intercept.

• Equation solvingRelated: Domain restrictions can rule out apparent solutions, especially with fractions and radicals.

• Friedrichs' inequalityRelated: The domain’s geometry and boundary help determine whether the estimate holds.

• Function of a real variableRelated: It specifies which real numbers a function can accept.

• Function of several real variablesRelated: Restrictions on valid input tuples determine where the function exists.

• Hartogs's theorem on separate holomorphicityRelated: The theorem's standard formulation assumes the function is defined on an open domain.

• Value (mathematics)Related: Only inputs in the domain can receive function values.