What is the range of f(x)=(2x)/(3x-1) ?

The range of f(x)=(2x)/(3x-1) is f(x) 2/3

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range of f(x)=(2x)/(3x-1)

range

f (x) = \frac{2 x}{3 x - 1}

f (x) < \frac{2}{3} or f (x) > \frac{2}{3}

Interval Notation

(- \infty, \frac{2}{3}) \cup (\frac{2}{3}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2 x}{3 x - 1}

Inverse of

\frac{2 x}{3 x - 1} : \frac{x}{3 x - 2}

\frac{x}{3 x - 2}

Find the domain of each inverse function

Domain of

\frac{x}{3 x - 2} : x < \frac{2}{3} or x > \frac{2}{3}

Combine the intervals

f (x) < \frac{2}{3} or f (x) > \frac{2}{3}

f (x) = x^{2} + \frac{1}{x}

(- 7, - 4), (3, - 2)

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

f (x) = - 10 + 8 x

f (x) = \frac{( - 16 + n )}{4}

What is the range of f(x)=(2x)/(3x-1) ?
The range of f(x)=(2x)/(3x-1) is f(x)< 2/3 \lor f(x)> 2/3