What is the inverse of f(x)=(1000)/(1+9e^{-x)} ?

The inverse of f(x)=(1000)/(1+9e^{-x)} is -ln((1000-x)/(9x))

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inverse of f(x)=(1000)/(1+9e^{-x)}

inverse

f (x) = \frac{1000}{1 + 9 e ^{- x}}

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

Solution steps

y = \frac{1000}{1 + 9 e ^{- x}}

Replace

x

with

y

x = \frac{1000}{1 + 9 e ^{- y}}

Solve for

y, x = \frac{1000}{1 + 9 e ^{- y}}

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

\frac{s - 4}{( s + 1 ) \cdot ( s + 2 )}

\frac{1}{2} lo g_{10} (6 x)

f (x) = 15 x + 5

f (x) = 15 x + 7

\frac{1}{x - 3}

What is the inverse of f(x)=(1000)/(1+9e^{-x)} ?
The inverse of f(x)=(1000)/(1+9e^{-x)} is -ln((1000-x)/(9x))