FunctionDomain

FunctionDomain[f,x]

finds the largest domain of definition of the real function f of the variable x.

FunctionDomain[f,x,dom]

considers f to be a function with arguments and values in the domain dom.

FunctionDomain[funs,vars,dom]

finds the largest domain of definition of the mapping funs of the variables vars.

FunctionDomain[{funs,cons},vars,dom]

finds the domain of funs with the values of vars restricted by constraints cons.

Details and Options

  • funs should be a list of functions of variables vars.
  • Possible values for dom are Reals and Complexes. The default is Reals.
  • If dom is Reals then all variables, parameters, constants, and function values are restricted to be real.
  • cons can contain equations, inequalities, or logical combinations of these.
  • The following options can be given:
  • GeneratedParametersChow to name parameters that are generated
    MethodAutomaticwhat method should be used
    WorkingPrecisionAutomaticprecision to be used in computations

Examples

open allclose all

Basic Examples  (2)

Find the largest domain of definition of a real function:

The largest domain of definition of a complex function:

Scope  (4)

Real univariate functions:

Domain restricted by constraints:

Complex univariate functions:

Real multivariate functions:

Complex multivariate functions:

Options  (2)

GeneratedParameters  (1)

FunctionDomain may introduce new parameters to represent the domain:

Use GeneratedParameters to control how the parameters are generated:

Method  (1)

By default, domains of real univariate functions are given in a reduced form:

Domains of other functions are not reduced:

Use Method to specify whether the domain should be given in a reduced form:

Possible Issues  (2)

All subexpressions of need to be real-valued for a point to belong to the real domain of :

Negative reals are not in the real domain of because is not real-valued:

is real-valued for all real :

The real domain information for mathematical functions is accurate up to lower-dimensional sets:

There is no full-dimensional subset of the space on which HankelH1 is real-valued:

Here is a 1-dimensional subset of the space on which HankelH1 is real-valued:

FunctionDomain is unable to detect that is real-valued:

Wolfram Research (2014), FunctionDomain, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionDomain.html.

Text

Wolfram Research (2014), FunctionDomain, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionDomain.html.

BibTeX

@misc{reference.wolfram_2020_functiondomain, author="Wolfram Research", title="{FunctionDomain}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/FunctionDomain.html}", note=[Accessed: 12-May-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_functiondomain, organization={Wolfram Research}, title={FunctionDomain}, year={2014}, url={https://reference.wolfram.com/language/ref/FunctionDomain.html}, note=[Accessed: 12-May-2021 ]}

CMS

Wolfram Language. 2014. "FunctionDomain." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FunctionDomain.html.

APA

Wolfram Language. (2014). FunctionDomain. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FunctionDomain.html