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

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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:

Introduced in 2014
 (10.0)