What is the range of (6x)/(7x-3) ?

The range of (6x)/(7x-3) is f(x) 6/7

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range of (6x)/(7x-3)

range

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 - 3}

Inverse of

\frac{6 x}{7 x - 3} : \frac{3 x}{7 x - 6}

\frac{3 x}{7 x - 6}

Find the domain of each inverse function

Domain of

\frac{3 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}

What is the range of (6x)/(7x-3) ?
The range of (6x)/(7x-3) is f(x)< 6/7 \lor f(x)> 6/7