help?

[u/MR_baldguy]

alright so basically we have 1 over x²+1

we make shure that x can't be equal to 1 or -1 stay with but why don't we do this

√x²≠√-1

x≠i

[u/Gold-Salamander4788]

because x²+1 can't be zero, right, but that only happens when x is i or -i, not 1 or -1

you're mixing up real and imaginary numbers, in the real numbers x² is always non-negative so x²+1 is always at least 1, never zero

the whole domain restriction thing is usually about real-valued functions so they don't even think about i, they just say the denominator never vanishes and call it a day

if you're working in the complex plane then yeah, you'd exclude i and -i, but for a basic calc class they're sticking to reals

[u/Southlander24]

Yes, x cannot be i or -i. That's why defining the domain of a function is so important. If the domain of x is the real numbers, then there are no singularities.

[u/matt7259]

First of all, context and formatting would really help.

Secondly, x can be -1 or 1, so are you sure you've recreated the question exactly?

Lastly, questions like this often are about real numbers only, and complex ones can be ignored.

[u/MezzoScettico]

You are correct that if x is allowed to be complex, then +-i are not allowed and aren't part of the domain.

If this is a domain question, you were probably told to restrict it to the real numbers at some point. That's usually the case in introductory algebra courses.