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

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range of 3/(x-1)

range

\frac{3}{x - 1}

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

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{3}{x - 1}

Inverse of

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

\frac{3}{x} + 1

Find the domain of each inverse function

Domain of

\frac{3}{x} + 1 : x < 0 or x > 0

Combine the intervals

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

d o main f (x) = \frac{x - 1}{x + 3}

mi d p o in t (1, - 9), (- 5, 0)

e x t re m e f (x) = 6 x^{2} - 24 x - 30

cr i t i c a l f (x) = \frac{2 x}{x ^{2} + 1}

s l o p e 3 x + y = 0