Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

moongazer Group Title

how do you get the domain of this:

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    http://www.wolframalpha.com/input/?i=domain+of+%E2%88%9A%28x%5E2+-+9x+%2B20%29%2F%E2%88%9A%28x%5E2+-+5x+%2B+6%29

    • 2 years ago
  2. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    how do you find it? step-by-step please :)

    • 2 years ago
  3. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    http://www.wolframalpha.com/input/?i=+%E2%88%9A%28x%5E2+-+9x+%2B20%29%2F%E2%88%9A%28x%5E2+-+5x+%2B+6%29

    • 2 years ago
  4. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    √(x^2 - 9x +20)/√(x^2 - 5x + 6) I already know the domain. But, how do you get it?

    • 2 years ago
  5. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    first workout contraints for squareroot : the thing inside squareroot cannot be negative

    • 2 years ago
  6. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    next work out constraints for denominator : denominator cannot be equal to 0

    • 2 years ago
  7. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    consider numerator first : \(\sqrt{x^2 - 9x +20}\)

    • 2 years ago
  8. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    can u work out domain for that ?

    • 2 years ago
  9. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    {x|x>=5} is that right?

    • 2 years ago
  10. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    somewhat right :) lets see how to solve

    • 2 years ago
  11. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    x^2-9x+20 >= 0 x^2-4x-5x+20 >=0 x(x-4) -5(x-4) >= 0 (x-4)(x-5) >= 0 x <= 4 or x >= 5

    • 2 years ago
  12. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    thats one constraint for numerator, lets find out the constraints for denominator

    • 2 years ago
  13. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ohhhh

    • 2 years ago
  14. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I think I am starting to understand it :)

    • 2 years ago
  15. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    good :) since, denominator is also under radical, it must be >=0 : x^2 - 5x + 6 >= 0 x^2-3x-2x + 6 >= 0 x(x-3) -2(x-3) >= 0 (x-2)(x-3) >= 0 x <= 2 or x >= 3

    • 2 years ago
  16. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    with those two things, we finished with the first step of finding constraints for radicals

    • 2 years ago
  17. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so far we have this : x <= 4 or x >= 5 x <= 2 or x >= 3

    • 2 years ago
  18. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yup, I understand it :)

    • 2 years ago
  19. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    next one is denominator can never equal to 0. so, x^2 - 5x + 6 \(\ne\) 0 x^2-3x-2x + 6 \(\ne\) 0 x(x-3) -2(x-3) \(\ne\) 0 (x-2)(x-3) \(\ne\) 0 x \(\ne\) 2 or x \(\ne\) 3

    • 2 years ago
  20. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    w8 Isn't it that it should be: x >= 4 or x >= 5 x >= 2 or x >= 3 ???

    • 2 years ago
  21. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    lets combine all constraints and make a meaningful constraint

    • 2 years ago
  22. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    which one ?

    • 2 years ago
  23. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    (x-4)(x-5) >= 0 (x-2)(x-3) >= 0

    • 2 years ago
  24. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    oh i got ur question, il give quick explanation

    • 2 years ago
  25. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you comfortable with parabola graph ?

    • 2 years ago
  26. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I think so

    • 2 years ago
  27. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    il show u in graph why its x <=4 , x >=5

    • 2 years ago
  28. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I know few things about parabola

    • 2 years ago
  29. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

    • 2 years ago
  30. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    im sketching this parabola : (x-4)(x-5) >= 0

    • 2 years ago
  31. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    it intersect x axis at 4, 5 right ?

    • 2 years ago
  32. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1348496600444:dw|

    • 2 years ago
  33. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    between 4 and 5, it is sinking down into x axis eh ?

    • 2 years ago
  34. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    its becoming NEGATIVE

    • 2 years ago
  35. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1348496705657:dw|

    • 2 years ago
  36. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    why did it intersect in x axis at 4, 5?

    • 2 years ago
  37. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    when u factored you got : (x-4)(x-5)

    • 2 years ago
  38. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    that means it intersects x-axis at 4 and 5

    • 2 years ago
  39. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ohh, ok what if it says (x-4)(x+5) does it intersect at 4 and -5 ?

    • 2 years ago
  40. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    thats right, when it says, (x-4)(x+5) = 0 then it intersects at 4 and -5

    • 2 years ago
  41. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    cuz for it to equal to 0, one of both of the factors must equal to 0

    • 2 years ago
  42. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1348498226449:dw|

    • 2 years ago
  43. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so the graph is like that?

    • 2 years ago
  44. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    perfect, thats (x-4)(x+5)

    • 2 years ago
  45. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    and the domain is x>=4,x<=-5 is it correct?

    • 2 years ago
  46. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    thats right ! you became expert ;p

    • 2 years ago
  47. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    for (x-4)(x+5)

    • 2 years ago
  48. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks! I know understand it. :) let's now continue with our previous discussion :)

    • 2 years ago
  49. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    great ! so far what we have

    • 2 years ago
  50. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    next one is denominator can never equal to 0. so, x^2 - 5x + 6 ≠ 0 x^2-3x-2x + 6 ≠ 0 x(x-3) -2(x-3) ≠ 0 (x-2)(x-3) ≠ 0 x ≠ 2 or x ≠ 3

    • 2 years ago
  51. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah we almost done

    • 2 years ago
  52. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    lets put down all the 3 constraints we got in one place :

    • 2 years ago
  53. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    1) numerator radical : x <= 4 or x >= 5 2) denominator radical : x <= 2 or x >= 3 3) denominator cant be 0 : x ≠ 2 or x ≠ 3

    • 2 years ago
  54. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I understand it. What's next?

    • 2 years ago
  55. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    see 2) and 3)

    • 2 years ago
  56. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    can we combine them as one, like this : 2) 3) : x < 2 or x > 3

    • 2 years ago
  57. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I'll be back just continue.

    • 2 years ago
  58. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    someone is calling me

    • 2 years ago
  59. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok after combining 2) and 3) we are left with : 1) numerator radical : x <= 4 or x >= 5 2) x < 2 or x > 3 this is the last step. see if u can figure out

    • 2 years ago
  60. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    out of x < 2 & x <= 4, x < 2 is more restrictive, so we have this in our domain : \(\color{green}{x < 2}\)

    • 2 years ago
  61. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    out of x > 3 & x <= 4 x > 3 , x <= 4 , which is same as : \(\color{green}{3<x\le 4}\)

    • 2 years ago
  62. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    and of course the last one, \(\color{green}{x >= 5}\)

    • 2 years ago
  63. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry for being away, I'm here again :)

    • 2 years ago
  64. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    np :) see if above stuff makes sense

    • 2 years ago
  65. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    it makes sense but why in the final answer they used "or" not "and" "," "then" or anything else dom K: {x|x<2 or 3<x<=4 or x>=5}

    • 2 years ago
  66. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah we always combine domain with "or" why ? cuz its meaningful. let me ask u a q

    • 2 years ago
  67. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    suppose we write : x < 2 and x >=5

    • 2 years ago
  68. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    for the domain it is ALWAYS "or" ?

    • 2 years ago
  69. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    is that possible ? can x be BOTH less than 2 and greater than 5 at the SAME time ha ?

    • 2 years ago
  70. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes always "or"

    • 2 years ago
  71. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, it is not possible

    • 2 years ago
  72. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    is "1" less than 2 and greater than "5" ?

    • 2 years ago
  73. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah, but if we put it like this : either "1" is less than 2 or greater than "5"

    • 2 years ago
  74. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    how meaningful it is, so while phrasing domain also, we use commonsense aswell :)

    • 2 years ago
  75. moongazer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, Thank you very much for helping me :)

    • 2 years ago
  76. ganeshie8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    np i learned as well. i forgot these long back in college... i enjoyed going thru these again.. thnks you too :)

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.