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moongazer Group Title

how do you get the domain of this:

  • one year ago
  • one year ago

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  1. moongazer Group Title
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    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

    • one year ago
  2. moongazer Group Title
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    how do you find it? step-by-step please :)

    • one year ago
  3. ganeshie8 Group Title
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    http://www.wolframalpha.com/input/?i=+%E2%88%9A%28x%5E2+-+9x+%2B20%29%2F%E2%88%9A%28x%5E2+-+5x+%2B+6%29

    • one year ago
  4. moongazer Group Title
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    √(x^2 - 9x +20)/√(x^2 - 5x + 6) I already know the domain. But, how do you get it?

    • one year ago
  5. ganeshie8 Group Title
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    first workout contraints for squareroot : the thing inside squareroot cannot be negative

    • one year ago
  6. ganeshie8 Group Title
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    next work out constraints for denominator : denominator cannot be equal to 0

    • one year ago
  7. ganeshie8 Group Title
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    consider numerator first : \(\sqrt{x^2 - 9x +20}\)

    • one year ago
  8. ganeshie8 Group Title
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    can u work out domain for that ?

    • one year ago
  9. moongazer Group Title
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    {x|x>=5} is that right?

    • one year ago
  10. ganeshie8 Group Title
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    somewhat right :) lets see how to solve

    • one year ago
  11. ganeshie8 Group Title
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    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

    • one year ago
  12. ganeshie8 Group Title
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    thats one constraint for numerator, lets find out the constraints for denominator

    • one year ago
  13. moongazer Group Title
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    ohhhh

    • one year ago
  14. moongazer Group Title
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    I think I am starting to understand it :)

    • one year ago
  15. ganeshie8 Group Title
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    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

    • one year ago
  16. ganeshie8 Group Title
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    with those two things, we finished with the first step of finding constraints for radicals

    • one year ago
  17. ganeshie8 Group Title
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    so far we have this : x <= 4 or x >= 5 x <= 2 or x >= 3

    • one year ago
  18. moongazer Group Title
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    yup, I understand it :)

    • one year ago
  19. ganeshie8 Group Title
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    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

    • one year ago
  20. moongazer Group Title
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    w8 Isn't it that it should be: x >= 4 or x >= 5 x >= 2 or x >= 3 ???

    • one year ago
  21. ganeshie8 Group Title
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    lets combine all constraints and make a meaningful constraint

    • one year ago
  22. ganeshie8 Group Title
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    which one ?

    • one year ago
  23. moongazer Group Title
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    (x-4)(x-5) >= 0 (x-2)(x-3) >= 0

    • one year ago
  24. ganeshie8 Group Title
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    oh i got ur question, il give quick explanation

    • one year ago
  25. ganeshie8 Group Title
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    you comfortable with parabola graph ?

    • one year ago
  26. moongazer Group Title
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    I think so

    • one year ago
  27. ganeshie8 Group Title
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    il show u in graph why its x <=4 , x >=5

    • one year ago
  28. moongazer Group Title
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    I know few things about parabola

    • one year ago
  29. moongazer Group Title
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    ok

    • one year ago
  30. ganeshie8 Group Title
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    im sketching this parabola : (x-4)(x-5) >= 0

    • one year ago
  31. ganeshie8 Group Title
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    it intersect x axis at 4, 5 right ?

    • one year ago
  32. ganeshie8 Group Title
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    |dw:1348496600444:dw|

    • one year ago
  33. ganeshie8 Group Title
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    between 4 and 5, it is sinking down into x axis eh ?

    • one year ago
  34. ganeshie8 Group Title
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    its becoming NEGATIVE

    • one year ago
  35. ganeshie8 Group Title
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    |dw:1348496705657:dw|

    • one year ago
  36. moongazer Group Title
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    why did it intersect in x axis at 4, 5?

    • one year ago
  37. ganeshie8 Group Title
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    when u factored you got : (x-4)(x-5)

    • one year ago
  38. ganeshie8 Group Title
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    that means it intersects x-axis at 4 and 5

    • one year ago
  39. moongazer Group Title
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    ohh, ok what if it says (x-4)(x+5) does it intersect at 4 and -5 ?

    • one year ago
  40. ganeshie8 Group Title
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    thats right, when it says, (x-4)(x+5) = 0 then it intersects at 4 and -5

    • one year ago
  41. ganeshie8 Group Title
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    cuz for it to equal to 0, one of both of the factors must equal to 0

    • one year ago
  42. moongazer Group Title
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    |dw:1348498226449:dw|

    • one year ago
  43. moongazer Group Title
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    so the graph is like that?

    • one year ago
  44. ganeshie8 Group Title
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    perfect, thats (x-4)(x+5)

    • one year ago
  45. moongazer Group Title
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    and the domain is x>=4,x<=-5 is it correct?

    • one year ago
  46. ganeshie8 Group Title
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    thats right ! you became expert ;p

    • one year ago
  47. moongazer Group Title
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    for (x-4)(x+5)

    • one year ago
  48. moongazer Group Title
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    Thanks! I know understand it. :) let's now continue with our previous discussion :)

    • one year ago
  49. ganeshie8 Group Title
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    great ! so far what we have

    • one year ago
  50. moongazer Group Title
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    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

    • one year ago
  51. ganeshie8 Group Title
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    yeah we almost done

    • one year ago
  52. ganeshie8 Group Title
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    lets put down all the 3 constraints we got in one place :

    • one year ago
  53. ganeshie8 Group Title
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    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

    • one year ago
  54. moongazer Group Title
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    I understand it. What's next?

    • one year ago
  55. ganeshie8 Group Title
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    see 2) and 3)

    • one year ago
  56. ganeshie8 Group Title
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    can we combine them as one, like this : 2) 3) : x < 2 or x > 3

    • one year ago
  57. moongazer Group Title
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    I'll be back just continue.

    • one year ago
  58. moongazer Group Title
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    someone is calling me

    • one year ago
  59. ganeshie8 Group Title
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    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

    • one year ago
  60. ganeshie8 Group Title
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    out of x < 2 & x <= 4, x < 2 is more restrictive, so we have this in our domain : \(\color{green}{x < 2}\)

    • one year ago
  61. ganeshie8 Group Title
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    out of x > 3 & x <= 4 x > 3 , x <= 4 , which is same as : \(\color{green}{3<x\le 4}\)

    • one year ago
  62. ganeshie8 Group Title
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    and of course the last one, \(\color{green}{x >= 5}\)

    • one year ago
  63. moongazer Group Title
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    sorry for being away, I'm here again :)

    • one year ago
  64. ganeshie8 Group Title
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    np :) see if above stuff makes sense

    • one year ago
  65. moongazer Group Title
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    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}

    • one year ago
  66. ganeshie8 Group Title
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    yeah we always combine domain with "or" why ? cuz its meaningful. let me ask u a q

    • one year ago
  67. ganeshie8 Group Title
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    suppose we write : x < 2 and x >=5

    • one year ago
  68. moongazer Group Title
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    for the domain it is ALWAYS "or" ?

    • one year ago
  69. ganeshie8 Group Title
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    is that possible ? can x be BOTH less than 2 and greater than 5 at the SAME time ha ?

    • one year ago
  70. ganeshie8 Group Title
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    yes always "or"

    • one year ago
  71. moongazer Group Title
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    yes, it is not possible

    • one year ago
  72. ganeshie8 Group Title
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    is "1" less than 2 and greater than "5" ?

    • one year ago
  73. ganeshie8 Group Title
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    yeah, but if we put it like this : either "1" is less than 2 or greater than "5"

    • one year ago
  74. ganeshie8 Group Title
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    how meaningful it is, so while phrasing domain also, we use commonsense aswell :)

    • one year ago
  75. moongazer Group Title
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    yes, Thank you very much for helping me :)

    • one year ago
  76. ganeshie8 Group Title
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    np i learned as well. i forgot these long back in college... i enjoyed going thru these again.. thnks you too :)

    • one year ago
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