Domain range

Quote:

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 $x:0<x<4$ will yield a negative value. Thus your domain is $\{-\infty,0]\cup[4,\infty)$ .

Part (b) is identical.