# What is the domain and range of the function g(x)=sqrt(x-1)?

##### 1 Answer
Mar 26, 2015

Hello,

• The domain of $g$ is [1,+infty[,
• The range of $g$ is [0,+infty[.

Indeed,

• A real number $x$ is in the domain $D$ if and only if $\sqrt{x - 1}$ exists, it means $x - 1 \ge 0$, or $x \ge 1$. Therefore D = [1,+oo[.

• The range is the set $V$ of all the values of the function $g$ :

1) Because $g \left(x\right)$ is a square root, $g \left(x\right) \ge 0$ : therefore, R subset [0,+oo[.

2) On the other hand, if $y \ge 0$, you can write $y = g \left(x\right)$ if you consider $x = {y}^{2} + 1$. Therefore [0,+oo[ subset R and finally R= [0,+oo[.

Graphically :

Domain is the projection of the curve of $g$ on x-axes
Range is the projection of the curve of $g$ on y-axes

graph{sqrt(x-1) [-1.75, 18.25, -1.88, 8.12]}