What is the range of-1/(x-3)-1 ?

The range of-1/(x-3)-1 is f(x) -1

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range of-1/(x-3)-1

range

- \frac{1}{x - 3} - 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 - 3} - 1

Inverse of

- \frac{1}{x - 3} - 1 : \frac{2 + 3 x}{x + 1}

\frac{2 + 3 x}{x + 1}

Find the domain of each inverse function

Domain of

\frac{2 + 3 x}{x + 1} : x < - 1 or x > - 1

Combine the intervals

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

\frac{x - 3}{x + 3}

f (x) = \frac{1}{4} sin (x - \frac{π}{4})

f (x) = - 6 + 6 x^{3}

f (x) = - 6 x^{2} + 4 x + 9

\frac{1}{6 - x}