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

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

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

range

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

f (x) < 1 or f (x) > 1

Interval Notation

(- \infty, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

\frac{3 x}{3 x - 1} : \frac{x}{3 ( x - 1 )}

\frac{x}{3 ( x - 1 )}

Find the domain of each inverse function

Domain of

\frac{x}{3 ( x - 1 )} : x < 1 or x > 1

Combine the intervals

f (x) < 1 or f (x) > 1

f (x) = 7 x^{3} - x

f (x) = t^{3} - 6 t^{2} + 9 t + 1

\frac{1 - 2 t}{4 + t}

f (x) = - x

f (x) = \frac{10 x ^{2} + 35 x}{49 x ^{2} - 28 x + 4}

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