What is the range of (6x)/(7x-1) ?

The range of (6x)/(7x-1) is f(x) 6/7

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range of (6x)/(7x-1)

range

\frac{6 x}{7 x - 1}

f (x) < \frac{6}{7} or f (x) > \frac{6}{7}

Interval Notation

(- \infty, \frac{6}{7}) \cup (\frac{6}{7}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{6 x}{7 x - 1}

Inverse of

\frac{6 x}{7 x - 1} : \frac{x}{7 x - 6}

\frac{x}{7 x - 6}

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < \frac{6}{7} or f (x) > \frac{6}{7}

f (x) = ln (\frac{( x + 1 )}{x ^{2} - 25})

x - \frac{y}{3} = 4

f (x) = x - 4

f (x) = \frac{3}{x + 2} + 2

(- 5, 1), (4, - 5)

What is the range of (6x)/(7x-1) ?
The range of (6x)/(7x-1) is f(x)< 6/7 \lor f(x)> 6/7