Given a mathematical function $f(x)$, we often want to know the set of $x$ values for which the function is defined. That set is called its domain. How can we compute the domain of $f(x)$ using mathematical software?
This answer assumes you have imported SymPy as follows.
1 2 from sympy import * # load all math functions init_printing( use_latex='mathjax' ) # use pretty math output
We also need to import another tool that SymPy doesn’t pull in by default.
1 from sympy.calculus.util import continuous_domain
We can then ask about a function’s domain. We provide the function, the variable we’re asking about, and the set of numbers we’re working inside of. For a simple one-variable function, we’re typically working in just the real numbers.
1 2 3 var( 'x' ) formula = 1 / ( x + 1 ) continuous_domain( formula, x, S.Reals )
$\displaystyle \left(-\infty, -1\right) \cup \left(-1, \infty\right)$
It’s sometimes easier to instead ask where the function is not defined. We can just ask for the complement of the domain.
1 2 domain = continuous_domain( formula, x, S.Reals ) Complement( S.Reals, domain )
The function is undefined only at $x=-1$.
Content last modified on 24 July 2023.
This website does not yet contain a solution for this task in any of the following software packages.
If you can contribute a solution using any of these pieces of software, see our Contributing page for how to help extend this website.