FunctionRange
FunctionRange[f,x,y]
finds the range of the real function f of the variable x returning the result in terms of y.
FunctionRange[f,x,y,dom]
considers f to be a function with arguments and values in the domain dom.
FunctionRange[funs,xvars,yvars,dom]
finds the range of the mapping funs of the variables xvars returning the result in terms of yvars.
FunctionRange[{funs,cons},xvars,yvars,dom]
finds the range of the mapping funs with the values of xvars restricted by constraints cons.
Details and Options

- funs should be a list of functions of variables xvars.
- funs and yvars must be lists of equal lengths.
- 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:
-
GeneratedParameters C how to name parameters that are generated Method Automatic what method should be used WorkingPrecision Automatic precision to be used in computations - With WorkingPrecision->Automatic, FunctionRange may use numerical optimization to estimate the range.
Examples
open allclose allScope (7)
Options (2)
Method (1)
By default, the results returned by FunctionRange may not be reduced:
Use Method to specify that the result should be given in a reduced form:
WorkingPrecision (1)
By default, FunctionRange attempts to compute exact results:
With finite WorkingPrecision, slower symbolic methods are not used:
Properties & Relations (1)
A function is surjective if its FunctionRange is True:
Use FunctionSurjective to test whether a functions is surjective:
Text
Wolfram Research (2014), FunctionRange, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionRange.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 2014. "FunctionRange." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FunctionRange.html.
APA
Wolfram Language. (2014). FunctionRange. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FunctionRange.html