What is the range of 1/(x-2)-3 ?

The range of 1/(x-2)-3 is f(x) -3

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range of 1/(x-2)-3

range

f (x) < - 3 or f (x) > - 3

Interval Notation

(- \infty, - 3) \cup (- 3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

\frac{1}{x - 2} - 3 : \frac{2 x + 7}{x + 3}

\frac{2 x + 7}{x + 3}

Find the domain of each inverse function

Domain of

\frac{2 x + 7}{x + 3} : x < - 3 or x > - 3

Combine the intervals

f (x) < - 3 or f (x) > - 3