help with finding the inverse

Question

anonymous · Answer

$$f(x)=\frac{ 100 }{ 1+2^{-x} }$$

anonymous · Answer

I changed x to y cross multiplied then divided by x and subtracted one to get

anonymous · Answer

$$2^{-x}=\frac{ 100 }{ x }-1$$

anonymous · Answer

took log base two and divide by negative one to get$$x=-(\log_{2}\frac{ 100 }{ x }-1) $$

oaktree · Answer

The inverse function is $$f^{-1}(x) = -\frac{ \log(\frac{ 100 }{ x } -1)}{ \log 2 }$$

oaktree · Answer

Which is exactly what you have there, except with the Change of Base added onto it so you don't have that ugly "log base 2".

anonymous · Answer

see my problem is in the back of my book I checked the answer and it says it is $$f ^{-1}(x)=\log_{2}(\frac{ x }{ 100-x }) $$

oaktree · Answer

Hum. That's odd. I double checked my answer on Mathematica 9, and I got what I wrote. Either Mathematica 9 is wrong (in which case I would be very worried indeed) or the textbook is wrong, which happens more often than you would think. So don't worry - you're almost certainly right.

anonymous · Answer

alright thanks for the double check man I appreciate it. I'll just ask my teacher tomorrow

oaktree · Answer

No problem, and thanks for the medal!