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

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

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

range

f (x) = \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) = 5 sin (- 2 x + \frac{π}{3})

3 k + 9 a = 75

f (x) = sin (6 x)

6 x + 10 y = 6

f (x) = tan (2 x - \frac{2 π}{3}) + 5

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