What is the range of f(x)= x/(x+4) ?

The range of f(x)= x/(x+4) is f(x) 1

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range of f(x)= x/(x+4)

range

f (x) = \frac{x}{x + 4}

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 + 4}

Inverse of

\frac{x}{x + 4} : - \frac{4 x}{x - 1}

- \frac{4 x}{x - 1}

Find the domain of each inverse function

Domain of

- \frac{4 x}{x - 1} : x < 1 or x > 1

Combine the intervals

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

(- 1, - 2), (3, 4)

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

\frac{2 x ^{2} - 3 x - 5}{2 x ^{2} - 5 x - 3}

\frac{\frac{x}{3}}{3}

What is the range of f(x)= x/(x+4) ?
The range of f(x)= x/(x+4) is f(x)<1\lor f(x)>1