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Formula of an inverse function

  1. Sep 9, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the formula of the inverse function of f(x)=300/(3+15e^.05x).

    2. Relevant equations


    3. The attempt at a solution

    I'm definitely way off but I got .05y(5x)+ln100=lnx. What I did was multiple the denominator by the y(cross mltiplication) and then tried to factor out e.
  2. jcsd
  3. Sep 9, 2014 #2


    Staff: Mentor

    Welcome to PF!

    So you start with y = 300 / (3 + 15 e^(x/20)

    and do the cross product trick to get y * (3 + 15e^(x/20)) = 300

    and then to:

    3 + 15e^(x/20) = 300 / y

    Does this help?

    You should now move terms and factors to the y side and you should then be able to isolate everything
    so that you get x = ...
  4. Sep 9, 2014 #3
    @Jedishrfu Thanks so much that was really helpful!! Last question do you know how you could be able to take the ln of e to simplify the equation?
  5. Sep 9, 2014 #4


    Staff: Mentor

    I'm sure he does. The real question is do you know how? If you do, take a stab at it.

    If you don't, review the properties of logarithms.
  6. Sep 9, 2014 #5


    Staff: Mentor

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