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Calculus/Inverse of a function

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Expert: Scotto - 8/27/2008


Question
Hi, my question is how do I find the inverse of
f(x)=e^x/(1+9e^x)?

Answer
Try taking the ln() of both sides.

The left side in the ln(f(x)).

The right side is the ln(e^x/(1+9e^x)),
which can be converted to ln(e^x) - ln(1+9e^x).

The ln() is the inverse of e^x, so the first term is x.

The second term, -ln(1+9e^x), could be approximated by -ln(9e^x), which reduces to -(ln(9)+ln(e^x)) = -(ln(9)+x).

I only see how an approximation to the inverse could be obtained by using the one I just gave you and putting them into the equation and solving for x.

If you find a way to do it, I'd be interested in hearing what it was.

Calculus

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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