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

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range of 2/(x+3)

range

\frac{2}{x + 3}

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{2}{x + 3}

Inverse of

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

\frac{2}{x} - 3

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = (x + 3)^{\frac{2}{3}}

y = x^{2} - x - 6

f (x) = \frac{4 x ^{2} + 2 x - 1}{2 x ^{3}}

f (x) = 4 x^{3} - 3 x^{2} - 6 x + 17

\frac{x ^{2} + 25}{x}