What is the range of (2x)/(x+5) ?

The range of (2x)/(x+5) is f(x) 2

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range of (2x)/(x+5)

range

\frac{2 x}{x + 5}

f (x) < 2 or f (x) > 2

Interval Notation

(- \infty, 2) \cup (2, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2 x}{x + 5}

Inverse of

\frac{2 x}{x + 5} : - \frac{5 x}{x - 2}

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

Find the domain of each inverse function

Domain of

- \frac{5 x}{x - 2} : x < 2 or x > 2

Combine the intervals

f (x) < 2 or f (x) > 2

(4, 14), (16, 4)

4 - x^{2}

f (x) = \frac{x ^{4} - 256}{2 x ^{2} - 8 x}

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

f (x) = \frac{4 x}{x ^{2} - 25}