Question

How do you find the domain for this particular function, 1/(x√(1-x^2))?

Answer 1

one thing to keep in mind with rationals and roots is that
when the fraction's denominator is 0, the fraction becomes undefined

when a radical or root inside value, becomes negative, and root is an even value, like 2 in this case
the root doesn't exist, or is "imaginary"

so for \(\bf \cfrac{1}{x\sqrt{1-x^2}}\)

those 2 restrictions apply
with that in mind ... what do you think the values "x" can take would be?

domain = values that "x" can safely take without jeopardizing the expression

Answer 2

So 0, 1 and -1 are forbidden. So I write the domain like: ]-inf;-1[ , ]-1;0[ , ]0;1[ , ]1;+inf[ ? (the square brackets mean "excluding" - French way, sorry if that was confusing :p)

Answer 3

yes, that's correct :)

Answer 4

Thank you very much!

Answer 5

yw