## DLS 2 years ago Domain of..sqrt{||x-1|-5|-2} ?

1. DLS

@wio

2. wio

$\bigg||x-1|-5\bigg|-2 > 0$

3. DLS

Correct,Next?

4. mathslover

$\sqrt{||x-1|-5|-2}$ better...

5. wio

Add 2 to both sides. Where areyou getting stuck?

6. DLS

I don't know how to deal with mod functions while solving for domain.

7. wio

where is the mod though?

8. DLS

mod/absolute bars

9. DLS

$\Huge \sqrt{||x-1|-5|-2}$

10. wio

so when you say 'mod' you mean the absolute value function?

11. DLS

Yes

12. wio

$|f(x)| < a\implies -a<f(x)<a\\ |f(x)| > a\implies a<f(x),\quad f(x)<-a\\$

13. wio

$\bigg||x-1|-5\bigg| >2 \implies |x-1|-5 < -2\quad\quad |x-1|-5 >2$

14. wio

The equations will keep splitting up and you'll have to keep track of all of them.

15. DLS

okay,ill try and let you know!

16. DLS

|x-1|<3 |x-1|>7

17. DLS

x-1<3 x-1<-3 x-1>7 x-1>-7 ?

18. DLS

x<4 x<-2 x>8 x>-6 ?

19. yrelhan4

x-1 > -3 *

20. yrelhan4

samajh aaya kyun?

21. DLS

hmm..yeah kinda

22. yrelhan4

x-1< -7 ** okay?

23. DLS

|x-1|<3 |x-1|>7 x-1<3 x-1>-3 x-1>7 x-1<-7

24. DLS

x<4 x>-2 x>8 x<-6

25. yrelhan4

yup. thats right i guess.

26. DLS

|dw:1364716179260:dw|

27. DLS

is it ? :o

28. DLS

ill do after this :/ thanks~

29. wio

looks like you messed up

30. wio

this is a really tedious problem man.

31. DLS

Give me a minute.

32. yrelhan4

hey wio. |x-1|<3 |x-1|>7 x-1<3 x-1>-3 x-1>7 x-1<-7 Thats right no?

33. wio

so far, that is right.

34. DLS

$\Huge||x-1|-5\bigg|-2 > 0$ ------->x<4 So lets take x as 3. Substituting, Okay positive. x>-2 So lets take x as -1. Substituting, Okay positive. x>8 So lets take x as 9. Substituting, Okay positive. x<-6 So lets take x as -7. Substituting, Okay positive. So that means all the solutions are acceptable.

35. yrelhan4

So, x<4, x<-6 --> x<-6 x>-2, x>8 --> x>8 right? @wio

36. wio

Looking at x<4 and x>-2 is enough to tell you all solutions work.

37. DLS

So drawing the wavy curve graph. |dw:1364716700507:dw|

38. wio

Wait, hold on...

39. wio

you've got: $-2<x<4\\ x<-6, \quad x>8$What happens at 5?

40. DLS

$\LARGE (-\infty,-5] U (8,\infty)$

41. DLS

oh ye to tera answer agaya :P @yrelhan4 lol

42. yrelhan4

^^^^

43. DLS

but its wrong :/

44. yrelhan4

:/

45. wio

Combining these equations: $-2<x<4\\ x<-6, \quad x>8$Makes me thing it's $$x\in (-\infty,-6)\cup (-2,4)\cup (8,\infty)$$

46. DLS

#genius^

47. DLS

still wrong :P

48. wio

Hmm, what are you using?

49. DLS

$x\in (-8,-6)\cup (-2,4)\cup (8,\infty)$ is the answer

50. yrelhan4

Put -10 in the question.. Its >0

51. wio

Yeah, that answer doesn't make sense.

52. DLS

i dont know how -8

53. DLS

i prefer @wio 's answer though,still we might be missing something maybe

54. wio

There would have to be some other thing limiting the domain.