Question

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

Answer 1

sqrt(a) is valid for all positive a values

Answer 2

so whatever makes the innards go less than zero is bad

Answer 3

Since it is a sqrt, you cannot have your value inside to be a negative.

So, this means that your x(x-2) >= 0

Answer 4

I plotted this function and I got:

Answer 5

that looks about right; since you got a quadratic in there its gonna act wierd like that

Answer 6

at 0 and 2 we have roots

<...........0.........2.........>
- + +
- - +
-------------------
+ - +

Domain: (-inf,0] or [2,inf)

Answer 7

can you show the work, please?

Answer 8

that is the work

Answer 9

the formulas. Analitically

Answer 10

Im really good at finding the domain graphically

Answer 11

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

Answer 12

x = 0 when x = 0

x-2 = 0 when x = 2

Answer 13

x>=0
x>=2

both inequalities are true

Answer 14

<...................0.................2................>
x<0; - x>0; + +
x<2; - - x>2; +
-------------------------------------
-*- = + +*-=- +*+=+

Answer 15

Domain: (-inf,0] or [2,inf)

Answer 16

ahhh got it