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

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

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

range

\frac{2 x}{x - 1}

f (x) < 2 or f (x) > 2

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2 x}{x - 1}

Inverse of

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

\frac{x}{x - 2}

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 2 or f (x) > 2

y = 5 x - x^{2}

f (x) = \frac{4}{5} x + 2

4 (x - 5)^{\frac{2}{3}}

f (x) = x + 4 - \frac{1 - x}{x}

f (x) = a x^{2}