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

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range of 3/(x-2)

range

\frac{3}{x - 2}

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{3}{x - 2}

Inverse of

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

\frac{3}{x} + 2

Find the domain of each inverse function

Domain of

\frac{3}{x} + 2 : x < 0 or x > 0

Combine the intervals

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

3 (y - 1) = 0

y = - x + 4

f (x) = 2 x + 3

(2, 3), (- 2, 1)

f (x) = 3^{x + 1}