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

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range of x/(x+1)

range

\frac{x}{x + 1}

f (x) < 1 or f (x) > 1

Interval Notation

(- \infty, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x}{x + 1}

Inverse of

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

- \frac{x}{x - 1}

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 1 or f (x) > 1

\frac{7 x - 4 y}{4} = x + 2

\frac{x ^{2} - 2}{x ^{2} - x - 2}

2 x + 6 y = 12, (1, 3)

f (x) = \frac{9}{100 - x ^{2}}

f (x) = \frac{1}{3 - x}