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osanseviero Group Title

Inverse logarithmic function

  • one year ago
  • one year ago

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

    • one year ago
  2. hartnn Group Title
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    yep, now isolate y

    • one year ago
  3. hartnn Group Title
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    \(\Large a=\ln c \implies c = e^a \)

    • one year ago
  4. osanseviero Group Title
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    \[y=\left( e ^{x} \right)^{2}\] the 2 can go down, right?

    • one year ago
  5. osanseviero Group Title
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    y=2e^x

    • one year ago
  6. hartnn Group Title
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    not actually

    • one year ago
  7. hartnn Group Title
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    \(\Large (e^x)^2 = e^{2x}\)

    • one year ago
  8. osanseviero Group Title
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    oops, another silly mistake

    • one year ago
  9. osanseviero Group Title
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    Can someone help me demostrate that (FoFinverse)(x)=(FinverseoF)(x)=x ?

    • one year ago
  10. hartnn Group Title
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    demonstrate ? you have a function for verifying that ?

    • one year ago
  11. osanseviero Group Title
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    The one we just did

    • one year ago
  12. osanseviero Group Title
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    \[\ln \sqrt{e ^{2x}} = e ^{2\ln \sqrt{x}}=x\]

    • one year ago
  13. hartnn Group Title
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    so, f inverse = e^2x just plug in x =ln \sqrt x oh, you did it :)

    • one year ago
  14. osanseviero Group Title
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    But how and why? (I think that was a good statement)

    • one year ago
  15. osanseviero Group Title
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    And how would that be x?

    • one year ago
  16. hartnn Group Title
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    ln x^m = m ln x

    • one year ago
  17. hartnn Group Title
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    ln e =1

    • one year ago
  18. hartnn Group Title
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    \(\sqrt {(e^x)^2} = |e^x| \\ \ln |e^x| = x \ln e = x\)

    • one year ago
  19. hartnn Group Title
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    ok ?

    • one year ago
  20. osanseviero Group Title
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    so the left one is kinda obvious, so it is x

    • one year ago
  21. osanseviero Group Title
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    Oh...and the other one is with \[a ^{logaN}=\]

    • one year ago
  22. osanseviero Group Title
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    N

    • one year ago
  23. hartnn Group Title
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    \(\huge a^{\log_aN}=N\)

    • one year ago
  24. hartnn Group Title
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    yes

    • one year ago
  25. osanseviero Group Title
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    :) Now I understand, thanks for fifth time, just one more question :P

    • one year ago
  26. hartnn Group Title
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    welcome ^_^

    • one year ago
  27. osanseviero Group Title
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    Which would be the domain and the range of the first, normal function?

    • one year ago
  28. hartnn Group Title
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    domain of ln sqrt x ?

    • one year ago
  29. hartnn Group Title
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    since its sqrt x, x>= 0 since its ln, sqrt x >0 in all, x>0

    • one year ago
  30. osanseviero Group Title
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    so the range of the inverse is x>0

    • one year ago
  31. osanseviero Group Title
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    Wish me good luck tomorrow

    • one year ago
  32. hartnn Group Title
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    yes! best of luck! hope you get full marks :)

    • one year ago
  33. osanseviero Group Title
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    I hope so, this will be a hard examn...all types of functions, trigonometric identities, operations with functions

    • one year ago
  34. hartnn Group Title
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    if you have practices enough, nothing is hard :)

    • one year ago
  35. osanseviero Group Title
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    Thanks for the help all night!

    • one year ago
  36. hartnn Group Title
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    you're welcome ^_^

    • one year ago
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