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

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

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

range

f (x) = \frac{1}{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{1}{x + 2} - 1

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = 5^{2 x - 1}

3 ln (sin (x)) \cdot sin (x)

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

f (x) = 6 x - 6

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

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