What is the range of (3x)/(7x-1) ?

The range of (3x)/(7x-1) is f(x) 3/7

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range of (3x)/(7x-1)

range

\frac{3 x}{7 x - 1}

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 - 1}

Inverse of

\frac{3 x}{7 x - 1} : \frac{x}{7 x - 3}

\frac{x}{7 x - 3}

Find the domain of each inverse function

Domain of

\frac{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}

5 x + 3

- 2 x^{2} + 14 x - 7

f (x) = 1 - 3 x^{2}

f (x) = \frac{x}{x ^{2} + 36}

f (x) = 2 cos (3 x + 2)

What is the range of (3x)/(7x-1) ?
The range of (3x)/(7x-1) is f(x)< 3/7 \lor f(x)> 3/7