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anonymous

  • one year ago

f(x) = 2e^3x + 1 Find the inverse f^-1(x). Can anyone help?

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  1. jackellyn
    • one year ago
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    Set it equal to y. Switch the x and the y, solve for y.

  2. jackellyn
    • one year ago
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    y=2x^3+1 x=2y^3+1 Solve for y.

  3. anonymous
    • one year ago
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    thx @jackellyn

  4. jackellyn
    • one year ago
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    Did you get the answer?

  5. anonymous
    • one year ago
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    my calculator is messing up, can you walk me through it pls. @jackellyn

  6. jackellyn
    • one year ago
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    so to solve for y you need to perform reverse operations. If we have x=2e^3y +1 What do we need to do first to get y alone?

  7. anonymous
    • one year ago
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    subtract 3y on both sides @jackellyn i think

  8. jackellyn
    • one year ago
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    Well the 3y is part of the exponent so we can't get rid of it just yet. First we need to get rid of the +1 and move it to the other side so do we add it to both sides or subtract it?

  9. anonymous
    • one year ago
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    subtract it @jackellyn

  10. jackellyn
    • one year ago
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    Right so we have x-1= 2e^3y Now we need to get rid of the 2 in front of the e^3y. What do you get?

  11. anonymous
    • one year ago
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    divided

  12. anonymous
    • one year ago
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    @jakellyn if thats correct

  13. anonymous
    • one year ago
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    @jackellyn you there

  14. jackellyn
    • one year ago
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    Yes, divide so then we have (x-1)/2=e^3y Do you remember the opposite operation of e?

  15. anonymous
    • one year ago
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    I don't recall @jackellyn

  16. jackellyn
    • one year ago
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    You need to take the natural log of both sides to get rid of the e and stay only with 3y. ln (x-1/2)=ln e^3y ln (x-1/2)=3y Solve for y.

  17. anonymous
    • one year ago
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    \[y =\frac{ x }{ 3}-\frac{ 1 }{ 6 }\] is that correct? @jackellyn

  18. anonymous
    • one year ago
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    so is this the inverse for \[f ^{-1}\]

  19. anonymous
    • one year ago
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    @jackellyn idk if you saw my replies^^^^

  20. jackellyn
    • one year ago
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    Sorry, I didnt. You can't get rid of the ln. It stays all together and then you can divide the 3. So \[y=\frac{(\ln \frac{ x-1 }{ 2 }) }{ 3 }\]

  21. anonymous
    • one year ago
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    so thats the inverse of \[f ^{-1}(x)\]

  22. jackellyn
    • one year ago
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    It is the inverse of f(x). \[f ^{-1}(x)\] is the notation for inverse.

  23. anonymous
    • one year ago
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    okay i understand now thx a lot

  24. anonymous
    • one year ago
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    @jackellyn one more question what is the inverse

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