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

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range of 1/(1-x)

range

\frac{1}{1 - x}

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

Interval Notation

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{1 - x}

Inverse of

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

- \frac{1 - x}{x}

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = \frac{- 21}{x ^{2} + 3}

f (x) = \frac{x - 14}{7}

f (x) = \frac{3}{4} x + 7

y = 5 x^{2} - 20 x + 2

f (x) = e^{x}