What is the range of (6x)/(x+7) ?

The range of (6x)/(x+7) is f(x) 6

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range of (6x)/(x+7)

range

\frac{6 x}{x + 7}

f (x) < 6 or f (x) > 6

Interval Notation

(- \infty, 6) \cup (6, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{6 x}{x + 7}

Inverse of

\frac{6 x}{x + 7} : - \frac{7 x}{x - 6}

- \frac{7 x}{x - 6}

Find the domain of each inverse function

Domain of

- \frac{7 x}{x - 6} : x < 6 or x > 6

Combine the intervals

f (x) < 6 or f (x) > 6

\frac{x}{x + 3}

x^{3} - 12 x + 1

y = 2.5 x, (2, 5)

y = \frac{x}{4} - 4, (- 8, 5)

2 x + 7 y = 13