What is the inverse of (1000)/(100+900e^{-x)} ?

The inverse of (1000)/(100+900e^{-x)} is -ln((10-x)/(9x))

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inverse of (1000)/(100+900e^{-x)}

inverse

\frac{1000}{100 + 900 e ^{- x}}

- ln (\frac{10 - x}{9 x})

Solution steps

y = \frac{1000}{100 + 900 e ^{- x}}

Replace

x

with

y

x = \frac{1000}{100 + 900 e ^{- y}}

Solve for

y, x = \frac{1000}{100 + 900 e ^{- y}}

- ln (\frac{10 - x}{9 x})

f (x) = \frac{x - 7}{x + 3}

\frac{x - 1}{x + 3}

f (x) = \frac{1}{3} x - 4

f (x) = e^{x - 4}

f (x) = 3 x^{2} - 4 x - 1

What is the inverse of (1000)/(100+900e^{-x)} ?
The inverse of (1000)/(100+900e^{-x)} is -ln((10-x)/(9x))