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

Dec 17, 2017

The domain is $x \in \left[1 , + \infty\right)$. The range is $g \left(x\right) \in \left[0 , + \infty\right)$

#### Explanation:

What's under the sqrt sign is $\ge 0$

Therefore,

$x - 1 \ge 0$

$x \ge 1$

The domain is

$x \in \left[1 , + \infty\right)$

When $x = 1$, $\implies$, $y = 0$

And

${\lim}_{x \to + \infty} g \left(x\right) = {\lim}_{x \to + \infty} \sqrt{x - 1} = + \infty$

The range is $g \left(x\right) \in \left[0 , + \infty\right)$

graph{sqrt(x-1) [-10, 10, -5, 5]}