Use continuity to show that a function is continuous on an interval Use the definition of continuity and the properties of limits to show that the function $g(x)= 2\sqrt{3-x}$ is continuous on the interval $(-\infty,3]$.
I know that for a function to be continuous, the limit of the function as $x$ approaches $a$ should be equal to $f(a)$.
So for the function $g(x)$ above to be continuous, the function should be continuous on the left of $3$ and at $3$.
But my problem is I don't know how to clearly present/write my answer.
Any help appreciated.
Thanks

The function is only left continous . 
You cannot apply the right hand limit as your domain doesnt allow you to take values greater then 3 .
