anonymous
  • anonymous
help with finding the inverse
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[f(x)=\frac{ 100 }{ 1+2^{-x} }\]
anonymous
  • anonymous
I changed x to y cross multiplied then divided by x and subtracted one to get
anonymous
  • anonymous
\[2^{-x}=\frac{ 100 }{ x }-1\]

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anonymous
  • anonymous
took log base two and divide by negative one to get\[x=-(\log_{2}\frac{ 100 }{ x }-1) \]
OakTree
  • OakTree
The inverse function is \[f^{-1}(x) = -\frac{ \log(\frac{ 100 }{ x } -1)}{ \log 2 }\]
OakTree
  • OakTree
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
  • anonymous
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
  • OakTree
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
  • anonymous
alright thanks for the double check man I appreciate it. I'll just ask my teacher tomorrow
OakTree
  • OakTree
No problem, and thanks for the medal!

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