What is the range of (4x)/(7x-5) ?

The range of (4x)/(7x-5) is f(x) 4/7

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range of (4x)/(7x-5)

range

\frac{4 x}{7 x - 5}

f (x) < \frac{4}{7} or f (x) > \frac{4}{7}

Interval Notation

(- \infty, \frac{4}{7}) \cup (\frac{4}{7}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{4 x}{7 x - 5}

Inverse of

\frac{4 x}{7 x - 5} : \frac{5 x}{7 x - 4}

\frac{5 x}{7 x - 4}

Find the domain of each inverse function

Domain of

\frac{5 x}{7 x - 4} : x < \frac{4}{7} or x > \frac{4}{7}

Combine the intervals

f (x) < \frac{4}{7} or f (x) > \frac{4}{7}

f (x) = \frac{2 x + 6}{x + 3}

\frac{3}{4} x - \frac{1}{2} y = \frac{1}{8}

- 2 x + 4 y = 0

f (x) = \frac{- 4 x ^{2} + 100}{5 x - 25}

y = x 3 - x

What is the range of (4x)/(7x-5) ?
The range of (4x)/(7x-5) is f(x)< 4/7 \lor f(x)> 4/7