What is the range of (7x)/(5x-6) ?

The range of (7x)/(5x-6) is f(x) 7/5

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range of (7x)/(5x-6)

range

\frac{7 x}{5 x - 6}

f (x) < \frac{7}{5} or f (x) > \frac{7}{5}

Interval Notation

(- \infty, \frac{7}{5}) \cup (\frac{7}{5}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{7 x}{5 x - 6}

Inverse of

\frac{7 x}{5 x - 6} : \frac{6 x}{5 x - 7}

\frac{6 x}{5 x - 7}

Find the domain of each inverse function

Domain of

\frac{6 x}{5 x - 7} : x < \frac{7}{5} or x > \frac{7}{5}

Combine the intervals

f (x) < \frac{7}{5} or f (x) > \frac{7}{5}

What is the range of (7x)/(5x-6) ?
The range of (7x)/(5x-6) is f(x)< 7/5 \lor f(x)> 7/5