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

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

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range of f(x)=(2x+3)/(x+1)

range

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

arcsin (x)

f (x) = \frac{x - 4}{2 x - 16}

y = 12 x - 4

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

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