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

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

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

inverse

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

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

Solution steps

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

Replace

t

with

x

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

Solve for

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

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

24

15

\frac{10 e ^{2 x} + 8}{4 + e ^{2 x}}

f (x) = \frac{5}{3 x + 4}

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