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

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

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range of (-1)/(x-1)-1

range

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

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{- 1}{x - 1} - 1

Inverse of

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

y = - 2 (x - 3) 2 + 5

y = \frac{x + 3}{x - 2}

f (x) = - 3 x + 12

x^{2} + 2 x - 1 - (2 x^{2} - 3 x + 6)

f (x) = \frac{1}{x ^{2} - 4 x - 12}

What is the range of (-1)/(x-1)-1 ?
The range of (-1)/(x-1)-1 is f(x)<-1\lor f(x)>-1