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

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range of x/(1+x)

range

\frac{x}{1 + x}

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}{1 + x}

Inverse of

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

(3, - 6), (5, 6)

f (x) = x^{\frac{1}{5}} + x

y = - \frac{5}{4} x + 1, (2, 7)

f (x) = - 8 x + 8

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