Calculating the range of $f(x)=\sqrt{2x-6}$. Please tell me how to calculate the range of $f(x)=\sqrt{2x-6}$? 
The solution in my math note says that the range of $f(x)$ is  $\lbrace y\in\mathbb{R}:y\ge 0\rbrace$.
As I followed this link  and do the sum, it gives me the range as $-\infty$ to $\infty$.
Please help me.

$$f(x)=\sqrt{2x-6}$$
$$g(x)=\sqrt x$$
Now, what is similarity in $f,g$?
If we substitute $x=(u+6)/2$ in $f$ we get $g(u)$
(Also square root function is always positive.So we get the +ve numbers only)
But $y^2=x$ have soltion $y=\pm \sqrt x$, but $f$ being a function is defined as $y+\sqrt x$. Yields only the positive part.
