# How do you find the domain and range for g(x)=sqrt(x-1)

How do you find the domain and range for $g\left(x\right)=\sqrt{x-1}$?
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ruinsraidy4
What's under the $\sqrt{}$ sign is $\ge 0$
Therefore,
$x-1\ge 0$
$x\ge 1$
The domain is
$x\in \left[1,+\mathrm{\infty }\right)$
When $x=1,⇒,y=0$
And
$\underset{x\to +\mathrm{\infty }}{lim}g\left(x\right)=\underset{x\to +\mathrm{\infty }}{lim}\sqrt{x-1}=+\mathrm{\infty }$
The range is $g\left(x\right)\mathrm{\infty }\left[0,+\mathrm{\infty }\right)$
graph{$\sqrt{x-1}\left[-10,10,-5,5\right]$}