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

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

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

range

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

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

Interval Notation

(- \infty, 2) \cup (2, \infty)

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

f (x) = x - e^{x}

f (x) = 7 x^{3} - 14 x^{2}

f (x) = \frac{( 2 x + 2 )}{( 4 x + 3 )}

f (x) = 1 - 4 x

f (x) = \frac{2}{3} x^{3}

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