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

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

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

range

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

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

f (x) = x - 5

(0) (4)

f (x) = \frac{1}{2 x ^{3}}

(4, - 5), (- 3, 6)

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