# Thread: Domain range

1. ## Domain range

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

2. Originally Posted by Oasis1993
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 $x$ such that $x(x-4)$ is positive will be in the domain of $\sqrt{x(x-4)}$.

Spoiler:
$x(x-4)$ has two zeroes at $x=0$ and $x=4$, so any value of $x:0 will yield a negative value. Thus your domain is $\{-\infty,0]\cup[4,\infty)$.

Part (b) is identical.