# How to figure out for which variables a function is real

I have

e[m_, n_] := Sqrt[m - n]


How can I figure out, using Mathematica, for which m and n the statement is a Real number?

• Assuming that $m$ and $n$ are real numbers themselves, Reduce[Sqrt[m - n] ∈ Reals, {m, n}, Reals]. Alternatively, get right of the Reals domain restriction in that command for a more general result. – MarcoB Nov 21 '16 at 16:56
• With version 10 or later: FunctionDomain[Sqrt[m - n], {m, n}] – Bob Hanlon Nov 21 '16 at 17:28

Here are two ways to do it.

MarcoB

Reduce[Sqrt[m - n] ∈ Reals, {m, n}, Reals]


n <= m

Bob Hanlon

FunctionDomain[Sqrt[m - n], {m, n}]


m - n >= 0