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

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

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

inverse

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

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

Solution steps

y = \frac{1}{1 - e ^{- x}}

Replace

x

with

y

x = \frac{1}{1 - e ^{- y}}

Solve for

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

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

9 x + 2 y - 18 = 0

(5, 9), (- 7, - 7)

f (x) = 13 x + 8

7 sin (5 x - 6)

(9.1) (2.9)

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