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

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Answer 1 · 2015-03-26T11:00:27

Hello,

Indeed,

A real number $x$ is in the domain $D$ if and only if $sqrt(x-1)$ exists, it means $x-1 >= 0$ , or $x>=1$ . Therefore $D = [1,+oo[$ .
The range is the set $V$ of all the values of the function $g$ :

1) Because $g(x)$ is a square root, $g(x) >= 0$ : therefore, $R subset [0,+oo[$ .

2) On the other hand, if $y>= 0$ , you can write $y = g(x)$ 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]}

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