Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

osanseviero

  • one year ago

Inverse logarithmic function

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

    So they want the inverse of \[F(x)=\ln \sqrt{x}\] So the inverse is \[x=\ln \sqrt{y}\]

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

    yep, now isolate y

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

    \(\Large a=\ln c \implies c = e^a \)

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

    \[y=\left( e ^{x} \right)^{2}\] the 2 can go down, right?

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

    y=2e^x

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

    not actually

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

    \(\Large (e^x)^2 = e^{2x}\)

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

    oops, another silly mistake

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

    Can someone help me demostrate that (FoFinverse)(x)=(FinverseoF)(x)=x ?

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

    demonstrate ? you have a function for verifying that ?

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

    The one we just did

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

    \[\ln \sqrt{e ^{2x}} = e ^{2\ln \sqrt{x}}=x\]

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

    so, f inverse = e^2x just plug in x =ln \sqrt x oh, you did it :)

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

    But how and why? (I think that was a good statement)

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

    And how would that be x?

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

    ln x^m = m ln x

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

    ln e =1

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

    \(\sqrt {(e^x)^2} = |e^x| \\ \ln |e^x| = x \ln e = x\)

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

    ok ?

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

    so the left one is kinda obvious, so it is x

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

    Oh...and the other one is with \[a ^{logaN}=\]

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

    N

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

    \(\huge a^{\log_aN}=N\)

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

    yes

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

    :) Now I understand, thanks for fifth time, just one more question :P

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

    welcome ^_^

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

    Which would be the domain and the range of the first, normal function?

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

    domain of ln sqrt x ?

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

    since its sqrt x, x>= 0 since its ln, sqrt x >0 in all, x>0

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

    so the range of the inverse is x>0

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

    Wish me good luck tomorrow

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

    yes! best of luck! hope you get full marks :)

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

    I hope so, this will be a hard examn...all types of functions, trigonometric identities, operations with functions

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

    if you have practices enough, nothing is hard :)

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

    Thanks for the help all night!

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

    you're welcome ^_^

  37. 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.