What is the range of 5/(e^{-x)-5} ?

The range of 5/(e^{-x)-5} is f(x) 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

range of 5/(e^{-x)-5}

range

\frac{5}{e ^{- x} - 5}

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

Interval Notation

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{5}{e ^{- x} - 5}

Inverse of

\frac{5}{e ^{- x} - 5} : - ln (\frac{5}{x} + 5)

- ln (\frac{5}{x} + 5)

Find the domain of each inverse function

Domain of

- ln (\frac{5}{x} + 5) : x < - 1 or x > 0

Combine the intervals

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

What is the range of 5/(e^{-x)-5} ?
The range of 5/(e^{-x)-5} is f(x)<-1\lor f(x)>0