What is the range of (8x)/(7x-3) ?

The range of (8x)/(7x-3) is f(x) 8/7

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range of (8x)/(7x-3)

range

\frac{8 x}{7 x - 3}

f (x) < \frac{8}{7} or f (x) > \frac{8}{7}

Interval Notation

(- \infty, \frac{8}{7}) \cup (\frac{8}{7}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{8 x}{7 x - 3}

Inverse of

\frac{8 x}{7 x - 3} : \frac{3 x}{7 x - 8}

\frac{3 x}{7 x - 8}

Find the domain of each inverse function

Domain of

\frac{3 x}{7 x - 8} : x < \frac{8}{7} or x > \frac{8}{7}

Combine the intervals

f (x) < \frac{8}{7} or f (x) > \frac{8}{7}

What is the range of (8x)/(7x-3) ?
The range of (8x)/(7x-3) is f(x)< 8/7 \lor f(x)> 8/7