Find the largest possible domain for the following funtions:
a) sqrt x(x-4)
b) sqrt 2x(x-4)
Thank you in advance for your help
Obviously, you can't have a negative sign under the square root.
So only values of $\displaystyle x$ such that $\displaystyle x(x-4)$ is positive will be in the domain of $\displaystyle \sqrt{x(x-4)}$.
Spoiler:
$\displaystyle x(x-4)$ has two zeroes at $\displaystyle x=0$ and $\displaystyle x=4$, so any value of $\displaystyle x:0<x<4$ will yield a negative value. Thus your domain is $\displaystyle \{-\infty,0]\cup[4,\infty)$.