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

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

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

range

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

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

Interval Notation

(- \infty, - \frac{1}{3}) \cup (- \frac{1}{3}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

- \frac{- 2 - x}{1 + 3 x} : x < - \frac{1}{3} or x > - \frac{1}{3}

Combine the intervals

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

(- 1, - 5), (- 3, 3)

5^{x}

f (x) = 8 (2 x^{2} - 1) - 2

f (x) = \frac{2 x ^{2} - 50}{x ^{2} + 5 x}

f (x) = x^{\frac{5}{2}} - 7 x^{2}

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