What is the inverse of f(x)=(100)/(1+2^{-x)} ?

The inverse of f(x)=(100)/(1+2^{-x)} is -(ln((100)/x-1))/(ln(2))

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inverse of f(x)=(100)/(1+2^{-x)}

inverse

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

- \frac{ln ( \frac{100}{x} - 1 )}{ln ( 2 )}

Solution steps

y = \frac{100}{1 + 2 ^{- x}}

Replace

x

with

y

x = \frac{100}{1 + 2 ^{- y}}

Solve for

y, x = \frac{100}{1 + 2 ^{- y}}

- \frac{ln ( \frac{100}{x} - 1 )}{ln ( 2 )}

What is the inverse of f(x)=(100)/(1+2^{-x)} ?
The inverse of f(x)=(100)/(1+2^{-x)} is -(ln((100)/x-1))/(ln(2))