Question

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

Answer 1

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

Answer 2

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.

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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