Question

How do I find the domain of the function `y=(1)/(sqrt(x-1))`?

Answer 1

`x in RR, x>1`

Explanation:

You cannot square root a negative, and you cannot divide by zero.

Other than this, this function works for all real values of x.

From this:

`x-1>0`
Because if `x=1, sqrt(x-1)=0` so we'd be dividing by a negative, which is a big no-no. Something similar goes for if `x<1`, since even `0.999-1=-0.0001<0` so we can't do this.
For any other real value, we are fine.

So the domain is:

`x in RR, x>1`