I'm trying to find the closed form expression from a question but I'm debating whether I should include $(-1)^x$ in it, which would make the question significantly easier. My problem with the question is that $(-1)^x$ becomes complex when $x$ is not an integer, i.e. most of its graph "vanishes". I'm not sure if something like this would be allowed in a high school level question but then again, there's no reason for it to not be allowed because other "vanishing" graphs like $\sqrt{x}$ and $\log_ax$ are standard and accepted.
What is the convention for $(-1)^x$ (given $x\in \Bbb{R}$) in closed form expressions? Is it considered an accepted part of closed form expressions even though it changes between being real and complex?
Thank you.
Note: To make it clearer, the question I'm referring to is part of the current IYMC so I decided to not include the question itself. Also, this is recreational work outside of school so I have no teacher to talk to. I wrote that the question is "high-school level" because of this but I'm not sure if it is.
Note 2: The question doesn't suggest anything about the answer, using $(-1)^x$, $x\in \Bbb{R}$ was a plan that I devised and I just wanted to know what the common practice for it is.
In calculus context the function $a^x$ is defined for $a>0$ even if the expression is well defined also when $a\le 0$ for particolar values of $x\in \mathbb{N}$ or $\mathbb{Q}$ as for example $(-1)^\frac13=-1$.