Theloshua one year ago Find the domain of the following functions

1. Theloshua

$f(x)=\frac{ \sqrt{x+2} }{ x-5 }$

2. Theloshua

$g(x)=\frac{ x-3 }{ \sqrt{x-1}}$

3. jim_thompson5910

how far did you get with any of these?

4. Theloshua

not far at all

5. Theloshua

like i need helpppp i haves so much work to do and so lil time, i dont wanna be up all nite...

6. jim_thompson5910

well first off, hopefully you see that x-5 in the denominator cannot be zero, so x-5 = 0 leads to x = 5 if x = 5, then the denominator x-5 is 0 that means x = 5 is NOT part of the domain

7. jim_thompson5910

agreed so far?

8. Theloshua

yes

9. jim_thompson5910

in the numerator of f(x), we have a radical you cannot take the square root of a negative number, so x+2 cannot be negative x+2 is either 0 or positive solve $\Large x+2 \ge 0$ for x. Tell me what you get

10. Theloshua

x greater or equal to -2

11. jim_thompson5910

yes

12. Theloshua

oh wait, i already solved for this one. i need help with the second

13. jim_thompson5910

so x cannot be 5 AND x has to be greater than or equal to -2

14. jim_thompson5910

same idea with g(x) you cannot divide by 0 and you cannot take the square root of a negative number

15. jim_thompson5910

what makes the denominator of g(x) equal to 0 ?

16. Theloshua

3 cant be an option

17. jim_thompson5910

why not?

18. Theloshua

because the top

19. Theloshua

you subtract -3

20. Theloshua

21. Theloshua

right?

22. jim_thompson5910

you can have 0 in the numerator though

23. jim_thompson5910

what do you get when you solve sqrt(x-1) = 0 for x?

24. Theloshua

1

25. jim_thompson5910

so if x = 1, then the whole denominator turns to 0 which is why x = 1 is NOT part of the domain

26. jim_thompson5910

also, you need to ensure that x-1 is never negative

27. Theloshua

okay

28. Theloshua

and the other part?

29. jim_thompson5910

solve x-1 >= 0 for x to get what?

30. Theloshua

1

31. jim_thompson5910

x = 1 ? or x <= 1 ? or x >= 1 ?

32. Theloshua

x greater than 1

33. jim_thompson5910

greater than or equal to 1, yes

34. jim_thompson5910

oh wait, nvm the "or equal to" part

35. jim_thompson5910

x cannot equal 1 because it leads to a division by zero error

36. Theloshua

okay

37. Theloshua

so? explaiiiin im confused tell me how to solve

38. jim_thompson5910

you just said it: the domain is x > 1

39. jim_thompson5910

any number larger than 1 will work as an input if x = 1 or smaller, then you run into problems

40. Theloshua

okay so the answer is x is not one and x is greater than 1?

41. jim_thompson5910

saying x > 1 implies that x is not equal to 1

42. jim_thompson5910

you don't need to say them both if you just say x > 1

43. Theloshua

okay, so thats the answer tho

44. jim_thompson5910

yes

45. Theloshua

thnxxxx

46. jim_thompson5910

no problem