What is the range of 6/(x+1) ?

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range of 6/(x+1)

range

\frac{6}{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{6}{x + 1}

Inverse of

\frac{6}{x + 1} : \frac{6}{x} - 1

\frac{6}{x} - 1

Find the domain of each inverse function

Domain of

\frac{6}{x} - 1 : x < 0 or x > 0

Combine the intervals

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

f (x) = \frac{1}{∣ 4 - 8 x ∣ + 12}

(1, 6), (5, - 2)

f (x) = \frac{1}{x - 2}

f (x) = 36 - x^{2} - x + 1

(3.58, 1.413), (4, 12.88)