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Math Help - finding the inverse of a function

  1. #1
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    finding the inverse of a function

    Algebraically find the inverse function of f(x)=9-3e^x
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    to find the inverse you switch x and y, and then solve for y.
    So do you know how to use ln's?
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  3. #3
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    no, could you please refresh my memory?
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    Quote Originally Posted by Asuhuman18 View Post
    no, could you please refresh my memory?
    Use the fact that if A = B^C then C = \log_B A. Please show what you've tried and say where you get stuck.
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  5. #5
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    Quote Originally Posted by Asuhuman18 View Post
    Algebraically find the inverse function of f(x)=9-3e^x
    HI

    let f^{-1}x=y

      x=f(y)

    x=9-3e^y

    3e^y=9-x

    Then apply take the log of both sides to the base e .
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  6. #6
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    so would it be f(x)=9-3e^x
    = ln(y)= ln(9)-3*ln(e^x)
    = ln(y)= ln(9)-3x
    this is where i get stuck if this is even right. I try to solve for x which would be (ln(y)-ln(9))/3=x right???
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  7. #7
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    Quote Originally Posted by Asuhuman18 View Post
    so would it be f(x)=9-3e^x
    = ln(y)= ln(9)-3*ln(e^x)
    = ln(y)= ln(9)-3x
    this is where i get stuck if this is even right. I try to solve for x which would be (ln(y)-ln(9))/3=x right???
    No. Please show every single step, starting from where you swap y and x. And please show how you used the crucial fact I mentioned in my earlier reply.

    Quote Originally Posted by mathaddict View Post
    HI

    let f^{-1}x=y

     x=f(y)

    x=9-3e^y

    3e^y=9-x

    Then apply take the log of both sides to the base e .
    I advise dividing by 3 first. Then use the result I gave in my earlier reply.
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  8. #8
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    i dont know how thats the PROBLEM!!!!!! I dont get your theorem either i did what i thought you asked me to do
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  9. #9
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    Quote Originally Posted by Asuhuman18 View Post
    i dont know how thats the PROBLEM!!!!!! I dont get your theorem either i did what i thought you asked me to do
    If you don't understand the rule I posted then you're strongly advised to go back a step and thoroughly review exponentials and logarithms before continuing with this problem. Understanding the relationship between them is crucial to understanding how to solve the problem you posted.
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