Formula of an inverse function

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Homework Help Overview

The problem involves finding the formula for the inverse function of f(x) = 300 / (3 + 15e^(0.05x)). The discussion centers around the manipulation of this function to isolate x in terms of y.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using cross multiplication to rearrange the equation and isolate terms involving y. There are attempts to simplify expressions using logarithmic properties, particularly concerning the natural logarithm of e.

Discussion Status

Some participants express gratitude for guidance received and seek further clarification on logarithmic simplifications. Multiple interpretations of the steps to isolate x are being explored, indicating an ongoing and productive discussion.

Contextual Notes

There is an indication of uncertainty regarding the manipulation of logarithmic expressions and the properties of logarithms, which may affect the progress of the discussion.

wertlewoo2
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Homework Statement


Find the formula of the inverse function of f(x)=300/(3+15e^.05x).


Homework Equations



f(x)=300/(3+15e^.05x)

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.
 
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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 = ...
 
@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?
 
wertlewoo2 said:
@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?
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.
 
Mark44 said:
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.

:smile:
 

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