# How do you find the range of x + sqrt( x-1 )?

The range is $\left[1 , + \infty\right)$
Set $f \left(x\right) = x + \sqrt{x - 1}$ this is defined for $x - 1 \ge 0 \implies x \ge 1$.Hence
the domain is $\left[1 , + \infty\right)$
$\left[f \left(1\right) , + \infty\right) = \left[1 , + \infty\right)$