Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Shido88

  • one year ago

Determine the Domain: y= sqrt (x-2)/2x-5 HELPPPP!!

  • This Question is Closed
  1. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    anybody ?

  2. amoodarya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1 Attachment
  3. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @amoodarya thanks for your help! but I really can't read what's going on :(

  4. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[y=\frac{\sqrt{x-2}}{2x-5}\]We'll start with all real numbers. We know that the square root of (x-2) will not give real results when x is less than 2, so let's restrict the range to\[2 \le x < \infty\]Now, we also know that x cannot be able value which will make the demonimator equal 0. So we'll say\[2x-5=0\]\[2x=5\]\[x=\frac{5}{2}\]So we know that x cannot be 5/2. Since that is greater than 2, we have to exclude it. The domain is then\[[2,\frac{5}{2}) \cup (\frac{5}{2}, \infty)\]

  5. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    give me a moment plz

  6. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the first part, how do you know x is less than 2 ?

  7. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i get the second part but no the first part

  8. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not*

  9. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can't you set up sqrt x-2 =0 and solve ?

  10. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, if x >2 then (x-2) is a positive number so the square root of (x-2) is a real number. Likewise, if x=2, then (x-2)=0, and sqrt(0)=0. However, if we take any number slightly smaller than 2, and let x equal that, say x=1.9999, (x-2) would be:\[(1.9999-2)=-0.0001\]And\[\sqrt{-0.0001}=\sqrt{-1 \times 0.0001}=\sqrt{-1} \times \sqrt{0.0001}=i \times 0.01\]and this is clearly not a real number. So the absolutely smallest value of x can be 2.

  11. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I see, thanks for the detailed answer!

  12. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're welcome! I hope my ramblings made sense. :)

  13. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    one more thing about this " [2,5/2)∪(5/2,∞)" how do you know which goes first and which goes last ? I mean the way to set it up ?

  14. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It does and thank you ! :D

  15. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, what do you mean by which goes first? Do you mean out of [2,5/2) and (5/2, infinity)?

  16. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  17. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that and which one is x and y ?

  18. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i thought the x that we found is 5/2 shouldn't that go first before the 2 ?

  19. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm sorry if I confuse you lol :[

  20. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think I see where the confusion is. \[[2,\frac{5}{2}) \cup (\frac{5}{2},\infty)\]is the same thing as\[x \in [2,\frac{5}{2})\]OR\[x \in (\frac{5}{2},\infty )\]That is, everything I wrote down represents the values that x is allowed to take. Neither of them refer to y.

  21. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It's set notation. I think\[2 \le x < \frac{5}{2}\]OR\[\frac{5}{2} < x < \infty\]would make more sense?

  22. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh yes!

  23. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok let me try the next problem! thank you so much!!

  24. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're very welcome! :)

  25. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey, are you still here?

  26. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I am stuck... lol

  27. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep

  28. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What's the problem?

  29. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is there to determine the domain and range using the graphing calculator ?

  30. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is there a way* excuse my typing..

  31. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Hmm, well I suppose you could graph the function and then look at the graph. Though sometimes it can be misleading if the window is set incorrectly.

  32. Shido88
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea

  33. Aylin
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You could probably also write a program on one to tell you the domain and range, but I'm terrible with coding.

  34. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.