What is the range of 3/x+2 ?

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range of 3/x+2

range

\frac{3}{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{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 < 2 or x > 2

Combine the intervals

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

r an g e f (x) = x + 2 - 3

mi d p o in t (13, 10), (3, - 2)

d o main f (x) = \frac{x - 2}{( x - 2 ) ^{2}}

e x t re m e f (x) = x^{4} - 8 x^{2} + 16

in v erse f (x) = 3 x + 2 - 1