What is the inverse of f(x)=(100000)/(100+900e^{-x)} ?

The inverse of f(x)=(100000)/(100+900e^{-x)} is -ln((1000-x)/(9x))

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inverse of f(x)=(100000)/(100+900e^{-x)}

inverse

f (x) = \frac{100000}{100 + 900 e ^{- x}}

- ln (\frac{1000 - x}{9 x})

Solution steps

y = \frac{100000}{100 + 900 e ^{- x}}

Replace

x

with

y

x = \frac{100000}{100 + 900 e ^{- y}}

Solve for

y, x = \frac{100000}{100 + 900 e ^{- y}}

- ln (\frac{1000 - x}{9 x})

f (x) = \frac{3 x}{x + 8}

f (x) = e^{2 - x}

f (x) = \frac{3 x}{x + 1}

f (x) = - \frac{2 x}{5}

f (x) = 36.5 - 2.5 x

What is the inverse of f(x)=(100000)/(100+900e^{-x)} ?
The inverse of f(x)=(100000)/(100+900e^{-x)} is -ln((1000-x)/(9x))