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

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range of 1/(x+1)

range

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

Inverse of

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

\frac{1}{x} - 1

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = \frac{x + 7}{x ^{2} - 14 x + 49}

9 x - 12 y = - 19

f (x) = x^{2} e^{x} - 4

3 x + y = 8

f (x) = \frac{- x ^{2}}{x ^{2} - 2 x + 8}