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anonymous

  • one year ago

pleases help me!!!!! Is it possible for x = −2 to be in the Domains of the functions a) R(x) =3x^3-5x+6/x+2 b) H(x)=√x+1 Explain why or why not for each function. What are the Domains of the functions R(x) and H(x)? If required, use inf for ∞.

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  1. anonymous
    • one year ago
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    if you plug -2 in for x in equation a what would you end up with in the denominator?

  2. anonymous
    • one year ago
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    4?

  3. anonymous
    • one year ago
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    -2 + 2 = ?

  4. anonymous
    • one year ago
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    0 sorry

  5. anonymous
    • one year ago
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    yep so if you divide by 0 what kind of answer does that give?

  6. anonymous
    • one year ago
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    0

  7. anonymous
    • one year ago
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    no, if you divide by zero the answer is "undefined"

  8. anonymous
    • one year ago
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    ok so knowing that, here is the definition of the domain of a function , from wikipedia, "the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined"

  9. anonymous
    • one year ago
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    so the domain is only inputs for which the function is defined, but for function a if we plug in a -2 then the answer is "undefined" so therefore is -2 in the domain of function a?

  10. anonymous
    • one year ago
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    so -2 cannot be the domain or either one,right?

  11. anonymous
    • one year ago
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    it cannot be in the domain of a for sure, because divide by zero is "undefined", what about function b?

  12. anonymous
    • one year ago
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    no i think

  13. anonymous
    • one year ago
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    because?

  14. anonymous
    • one year ago
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    because it'd leave u with an irrational right?

  15. anonymous
    • one year ago
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    well it would leave you with a complex/imaginary number which technically i think would be in the domain, but i think the answer your teacher is looking for is that is NOT in the domain

  16. anonymous
    • one year ago
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    ok good so you have the first question done what about the second part, what are the domains of each function?

  17. anonymous
    • one year ago
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    i dont know

  18. anonymous
    • one year ago
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    ok so lets look at equation b first, what type of numbers for x would give us a complex/imaginary answer?

  19. anonymous
    • one year ago
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    negative numbers

  20. anonymous
    • one year ago
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    correct, so the domain would be all numbers 0 or greater, right?

  21. anonymous
    • one year ago
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    yes

  22. anonymous
    • one year ago
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    perfect so that would look like this x greater than or equal to 0

  23. anonymous
    • one year ago
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    now how about equation a, there is only one number, -2, that would give us a divide by zero

  24. anonymous
    • one year ago
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    so what would the domain look like for a?

  25. anonymous
    • one year ago
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    x<-2?

  26. anonymous
    • one year ago
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    yes but also greater than -2

  27. anonymous
    • one year ago
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    i think you need to write both answers in interval notation

  28. anonymous
    • one year ago
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    can you write this in interval notation? x is all numbers less than -2 and all numbers greater than -2

  29. anonymous
    • one year ago
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    i get A but not B

  30. anonymous
    • one year ago
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    oh, good, what did you get for A?

  31. anonymous
    • one year ago
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    a: [0,inf)

  32. anonymous
    • one year ago
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    hmm thats the answer for b

  33. anonymous
    • one year ago
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    whoops yeah, i get B but not A

  34. anonymous
    • one year ago
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    oh ok

  35. anonymous
    • one year ago
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    so b, you need to use a union symbol

  36. anonymous
    • one year ago
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    looks like a U

  37. anonymous
    • one year ago
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    how would you show all numbers less than -2?

  38. anonymous
    • one year ago
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    wait, just got completely confused

  39. anonymous
    • one year ago
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    k

  40. anonymous
    • one year ago
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    okay sorry bout that

  41. anonymous
    • one year ago
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    no prob, ok so for a lets do that in two steps, how can you show that x is all numbers less than -2?

  42. anonymous
    • one year ago
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    x<-2

  43. anonymous
    • one year ago
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    i mean in interval notation

  44. anonymous
    • one year ago
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    like this (-inf, -2)

  45. anonymous
    • one year ago
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    ok but x is also all numbers greater than -2

  46. anonymous
    • one year ago
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    so we need to write it like this (-inf, -2) U (-2, inf)

  47. anonymous
    • one year ago
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    does this make sense?

  48. anonymous
    • one year ago
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    yes, theres brackets on -2 tho,right?

  49. anonymous
    • one year ago
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    there is not brackets on the -2 because -2 is not included in the domain

  50. anonymous
    • one year ago
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    okay

  51. anonymous
    • one year ago
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    so since its not included we use parenthesis

  52. anonymous
    • one year ago
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    nice, all done :)

  53. anonymous
    • one year ago
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    i thnk i got it, thanks so much!

  54. anonymous
    • one year ago
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    yw

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