find the domain of the function f of x equals 1 divided by the square root of 1 minus X

Question

kirbykirby · Answer

$$ f(x)=\frac{1}{\sqrt{1-x}}$$?

kirbykirby · Answer

Since you can't divide by 0, you need the denominator to be not equal to 0, i.e.
$$ \sqrt{1-x}\ne0$$ Furthermore, whatever is under the square root should be positive, so you require:
$$ \sqrt{1-x}>0$$. Then you just have to solve this inequality.

kirbykirby · Answer

(Notice that the requirement of $> 0$ also encompasses the requirement of $\ne 0$)

anonymous · Answer

That's what I thought but the test I'm studying for says the answer is X<1. Thanks for your help.

kirbykirby · Answer

yes once you simplify the inequality, you will get x < 1

kirbykirby · Answer

1 - x > 0
-x > -1
x < 1