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

osanseviero

Inverse logarithmic function

  • 6 months ago
  • 6 months ago

  • This Question is Closed
  1. osanseviero
    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 \[x=\ln \sqrt{y}\]

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

    yep, now isolate y

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

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

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

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

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

    y=2e^x

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

    not actually

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

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

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

    oops, another silly mistake

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

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

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

    demonstrate ? you have a function for verifying that ?

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

    The one we just did

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

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

    • 6 months ago
  13. hartnn
    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 :)

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

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

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

    And how would that be x?

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

    ln x^m = m ln x

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

    ln e =1

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

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

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

    ok ?

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

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

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

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

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

    N

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

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

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

    yes

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

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

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

    welcome ^_^

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

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

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

    domain of ln sqrt x ?

    • 6 months ago
  29. hartnn
    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

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

    so the range of the inverse is x>0

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

    Wish me good luck tomorrow

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

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

    • 6 months ago
  33. osanseviero
    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

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

    if you have practices enough, nothing is hard :)

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

    Thanks for the help all night!

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

    you're welcome ^_^

    • 6 months 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.