What is the range of x/(1-x) ?

The range of x/(1-x) is f(x) -1

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range of x/(1-x)

range

\frac{x}{1 - x}

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

Interval Notation

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x}{1 - x}

Inverse of

\frac{x}{1 - x} : \frac{x}{x + 1}

\frac{x}{x + 1}

Find the domain of each inverse function

Domain of

\frac{x}{x + 1} : x < - 1 or x > - 1

Combine the intervals

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

e^{- 1.5 x^{2}}

3 - e^{2 x}

f (x) = \frac{( x + 9 )}{x ^{2} + 4 x}

x^{5} - 4 x^{3}

f (x) = x^{3} - x^{2} - x - 10