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

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

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range of y= 2/(x+2)+1

range

y = \frac{2}{x + 2} + 1

f (x) < 1 or f (x) > 1

Interval Notation

(- \infty, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

\frac{2}{x + 2} + 1 : \frac{- 2 x + 4}{x - 1}

\frac{- 2 x + 4}{x - 1}

Find the domain of each inverse function

Domain of

\frac{- 2 x + 4}{x - 1} : x < 1 or x > 1

Combine the intervals

f (x) < 1 or f (x) > 1

f (x) = - 2 x^{4} + 5 x^{2}

(1, - 7), (- 3, - 8)

3 sin (x)

f (x) = - 2 x + 4 + 3

\frac{1}{x + 19}

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