What is the range of 1/(1-e^{-x)} ?

The range of 1/(1-e^{-x)} is f(x) 1

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range of 1/(1-e^{-x)}

range

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

f (x) < 0 or f (x) > 1

Interval Notation

(- \infty, 0) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

\frac{1}{1 - e ^{- x}} : - ln (- \frac{1 - x}{x})

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

Find the domain of each inverse function

Domain of

- ln (- \frac{1 - x}{x}) : x < 0 or x > 1

Combine the intervals

f (x) < 0 or f (x) > 1

f (x) = 8 - x

f (x) = \frac{x ^{2} - 2 x - 1}{x + 1}

\frac{e ^{x}}{x}

f (x) = \frac{5}{x ^{2} - 9 x - 22}

f (x) = 14 x^{2}

What is the range of 1/(1-e^{-x)} ?
The range of 1/(1-e^{-x)} is f(x)<0\lor f(x)>1