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

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range of 1/(x+3)

range

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

Inverse of

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

\frac{1}{x} - 3

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = \frac{x ^{3} - 7}{2}

4 x^{2}, x \leq 0

(0, 1), (1, 0)

(7.14) (- 1.9)

(1, 1), (4, - \frac{1}{2})