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

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

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

range

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

f (x) < \frac{3}{8} or f (x) > \frac{3}{8}

Interval Notation

(- \infty, \frac{3}{8}) \cup (\frac{3}{8}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < \frac{3}{8} or f (x) > \frac{3}{8}

\frac{x - 4}{3 x - x ^{2}}

f (x) = 2 x^{2} + 3 x - 5

(x - 3)^{2}

f (x) = 4 x^{2} - 40 x + 98

f (x) = - x + 5 y = - 9

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