Can someone teach me how to find the domain of an expression: sqrt(x(x-2))

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Can someone teach me how to find the domain of an expression: sqrt(x(x-2))

Mathematics
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sqrt(a) is valid for all positive a values
so whatever makes the innards go less than zero is bad
Since it is a sqrt, you cannot have your value inside to be a negative. So, this means that your x(x-2) >= 0

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I plotted this function and I got:
1 Attachment
that looks about right; since you got a quadratic in there its gonna act wierd like that
at 0 and 2 we have roots <...........0.........2.........> - + + - - + ------------------- + - + Domain: (-inf,0] or [2,inf)
can you show the work, please?
that is the work
the formulas. Analitically
Im really good at finding the domain graphically
sqrt[x(x-2)] is already factored out .... i really cant see much else to do with it other than plot it on a number line and show the +- ranges
x = 0 when x = 0 x-2 = 0 when x = 2
x>=0 x>=2 both inequalities are true
<...................0.................2................> x<0; - x>0; + + x<2; - - x>2; + ------------------------------------- -*- = + +*-=- +*+=+
Domain: (-inf,0] or [2,inf)
ahhh got it

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