help with verifying an inverse

help with verifying an inverse

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so i have \[f(x)=\frac{ 100 }{ 1+2^{-x} }\] and \[f ^{-1}(x)=-\log_{2}(\frac{ 100 }{ x } -1)-1\]

I need help with \[(f o f ^{-1})x=x\]

because after I distribute the negative I am not sure what to do with the log in the exponent of 2

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