What is the range of (x^2+x-6)/(x^2+6x+9) ?

The range of (x^2+x-6)/(x^2+6x+9) is f(x) 1

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range of (x^2+x-6)/(x^2+6x+9)

range

\frac{x ^{2} + x - 6}{x ^{2} + 6 x + 9}

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{x ^{2} + x - 6}{x ^{2} + 6 x + 9}

Inverse of

\frac{x ^{2} + x - 6}{x ^{2} + 6 x + 9} : \frac{- 2 - 3 x}{x - 1}

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

Find the domain of each inverse function

Domain of

\frac{- 2 - 3 x}{x - 1} : x < 1 or x > 1

Combine the intervals

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

f (x) = 4 (x + 3)^{2} - 16

2 x - 3

x^{2} + 12

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

f (x) = x^{9}

What is the range of (x^2+x-6)/(x^2+6x+9) ?
The range of (x^2+x-6)/(x^2+6x+9) is f(x)<1\lor f(x)>1