Range of $\sqrt{x-1}$ Problem: 


  Find the range of $f(x)=\sqrt{x-1}$


Now the problem I face is this: is the range $[0,\infty),$ or is it $(-\infty,\infty)$? $$$$I had learnt that $\sqrt{x^2} = \pm x$. However, on the Net, I read that $\sqrt{x^2}=|x|$ ie the output of a square root function is positive. If the output of a square root is always positive then the Range of  $\sqrt{x-1}$ is obviously $[0, \infty)$ $$$$

I would be very grateful for any help in clearing this doubt. Thanks very, very much in advance!
$\sqrt{z}$ is a function(Maps a point to a single point). So $\sqrt{z^2}$can only take a single value. By convention, $\sqrt{z}\ge0$. So,$\sqrt{z^2}=|z|$. So to answer your question, range will be $[0,\infty)$
for square root function to be defined x-1>=0,or x>=1 there for the range of function is [0,+inf)