What is the range of (-x^2+x+12)/(x^2+4x-32) ?

The range of (-x^2+x+12)/(x^2+4x-32) is f(x)>-1

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range of (-x^2+x+12)/(x^2+4x-32)

range

\frac{- x ^{2} + x + 12}{x ^{2} + 4 x - 32}

f (x) > - 1

Interval Notation

(- 1, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{- x ^{2} + x + 12}{x ^{2} + 4 x - 32} : x < - 8 or - 8 < x < 4 or x > 4

Simplify

\frac{- x ^{2} + x + 12}{x ^{2} + 4 x - 32} : - \frac{x + 3}{x + 8}

Extreme Points of

- \frac{x + 3}{x + 8} :

None

Find the range for the interval

- \infty < x < - 8 : - 1 < f (x) < \infty

Find the range for the interval

- 8 < x < 4 : - \frac{7}{12} < f (x) < \infty

Find the range for the interval

4 < x < \infty : - 1 < f (x) < - \frac{7}{12}

Combine the ranges of all domain intervals to obtain the function range

f (x) > - 1 or f (x) > - \frac{7}{12} or - 1 < f (x) < - \frac{7}{12}

f (x) > - 1

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

f (x) = x^{3} - 75 x

(- 2 - 6) 0

f (x) = (x - 3) (x + 6)

sec (x) - csc (x)

What is the range of (-x^2+x+12)/(x^2+4x-32) ?
The range of (-x^2+x+12)/(x^2+4x-32) is f(x)>-1