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

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

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

range

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

x + 1

f (x) = 0.1 x^{2} + 91 x + 3100

\frac{e ^{x - 3}}{x - 2}

- 6 + 6 x^{3}

f (x) = 5 x + 9

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