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

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

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range of 3/(x+1)+2

range

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

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{3}{x + 1} + 2

Inverse of

\frac{3}{x + 1} + 2 : \frac{- x + 5}{x - 2}

\frac{- x + 5}{x - 2}

Find the domain of each inverse function

Domain of

\frac{- x + 5}{x - 2} : x < 2 or x > 2

Combine the intervals

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

f (x) = \frac{5 x}{4 x - 5}

ln (x + 1)

x - 3 + x^{2} - 16

(- 5, 4), (0, - 2)

\frac{3 x ^{2}}{x - 5}