What is the range of 1/x-2 ?

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range of 1/x-2

range

\frac{1}{x} - 2

f (x) < - 2 or f (x) > - 2

Interval Notation

(- \infty, - 2) \cup (- 2, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{x} - 2

Inverse of

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

\frac{1}{x + 2}

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < - 2 or f (x) > - 2

f (x) = \frac{3 x ^{2} - 12 x}{x ^{2} - 5 x + 4}

- 7 x - 4 y = - 12

x^{2} - 9

(- 2.1) (4.6)

y = 2 x - 1