Hi, im trying to find the domain of $\displaystyle f(x)=arcsin(1/x)$

I know that $\displaystyle y=arcsinx$ is defined on the interval (-1,1),

so when I look at f(x) then (1/x) should be on the interval:

$\displaystyle -1<=(1/x)<=1$

I know that the solution is $\displaystyle x>=1$ and $\displaystyle x<=-1$ (x is bigger or equal to 1, and less or equal to -1) But I dont know how they got there? any help? thanks!