## anonymous 5 years ago Can someone teach me how to find the domain of an expression: sqrt(x(x-2))

1. amistre64

sqrt(a) is valid for all positive a values

2. amistre64

so whatever makes the innards go less than zero is bad

3. anonymous

Since it is a sqrt, you cannot have your value inside to be a negative. So, this means that your x(x-2) >= 0

4. anonymous

I plotted this function and I got:

5. amistre64

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

6. amistre64

at 0 and 2 we have roots <...........0.........2.........> - + + - - + ------------------- + - + Domain: (-inf,0] or [2,inf)

7. anonymous

can you show the work, please?

8. amistre64

that is the work

9. anonymous

the formulas. Analitically

10. anonymous

Im really good at finding the domain graphically

11. amistre64

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

12. amistre64

x = 0 when x = 0 x-2 = 0 when x = 2

13. anonymous

x>=0 x>=2 both inequalities are true

14. amistre64

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

15. amistre64

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

16. anonymous

ahhh got it