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

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

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

range

f (x) = \frac{3 x}{7 x - 6}

f (x) < \frac{3}{7} or f (x) > \frac{3}{7}

Interval Notation

(- \infty, \frac{3}{7}) \cup (\frac{3}{7}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

\frac{6 x}{7 x - 3} : x < \frac{3}{7} or x > \frac{3}{7}

Combine the intervals

f (x) < \frac{3}{7} or f (x) > \frac{3}{7}

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