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anonymous

  • one year ago

Given f(x)=log11x, find f–1(x) and f–1(2).

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  1. anonymous
    • one year ago
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    \[given f(x)=\log_{11} x, find f ^{-1}(x) and f ^{-1}(2)\]

  2. anonymous
    • one year ago
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    Can anyone help?

  3. SolomonZelman
    • one year ago
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    u can use ~ for space

  4. SolomonZelman
    • one year ago
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    An inverse of logarithmic is going to be an exponential.

  5. anonymous
    • one year ago
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    Inverse?

  6. SolomonZelman
    • one year ago
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    \({\rm f}^{-1}(x)\) is a notation for an inverse function.

  7. anonymous
    • one year ago
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    Oh okay.. I suck at these to be honest

  8. SolomonZelman
    • one year ago
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    Your function is: \(\large\color{black}{ \displaystyle f(x)=\log_{11}(x) }\) 1) replace f(x) with y. 2) switch x and y (write y instead of x, and write y instead of x) 3) {solve for/ isolate the} y.

  9. anonymous
    • one year ago
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    \[x=\log_{11} y\]

  10. anonymous
    • one year ago
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    like that?

  11. SolomonZelman
    • one year ago
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    for the third step, you will need to know that \(\Large\color{black}{ \displaystyle \color{red}{\rm a}=\log_{\color{green}{\rm b}}(\color{blue}{\rm c}) ~~~~\Longrightarrow~~~~\color{green}{\rm b}^\color{red}{\rm a}=\color{blue }{\rm c} }\).

  12. SolomonZelman
    • one year ago
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    yes, for the first two steps, that is correct

  13. SolomonZelman
    • one year ago
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    now, apply the third step to that (to \(x=\log_{11}y\) )

  14. anonymous
    • one year ago
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    \[11^{x}\]

  15. anonymous
    • one year ago
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    =y

  16. anonymous
    • one year ago
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    \[11^{x}=y\] Like that? @SolomonZelman

  17. SolomonZelman
    • one year ago
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    yes

  18. SolomonZelman
    • one year ago
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    then replcae y by \(f^{-1}(x)\)

  19. SolomonZelman
    • one year ago
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    |dw:1435782711063:dw|

  20. SolomonZelman
    • one year ago
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    then for f\(^{-1}\)(2) plug in 2 for x, into the last expression that I drew

  21. anonymous
    • one year ago
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    where did you get the 2 from?

  22. SolomonZelman
    • one year ago
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    you need \(f^{-1}(2)\). that is your second part.

  23. anonymous
    • one year ago
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    ohhh okay I got it now

  24. anonymous
    • one year ago
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    Can you help me with another one? @SolomonZelman

  25. SolomonZelman
    • one year ago
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    ok, but I am helping another person right now... well I am attempting to help that person.

  26. SolomonZelman
    • one year ago
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    will see.

  27. anonymous
    • one year ago
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    Okay.. I'll just open a new question.

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