What is the domain of f(x)=(6x-x^2)/(x^2+4x-12) ?

The domain of f(x)=(6x-x^2)/(x^2+4x-12) is x 2

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domain of f(x)=(6x-x^2)/(x^2+4x-12)

domain

f (x) = \frac{6 x - x ^{2}}{x ^{2} + 4 x - 12}

x < - 6 or - 6 < x < 2 or x > 2

Interval Notation

(- \infty, - 6) \cup (- 6, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 2, x = - 6

The function domain

x < - 6 or - 6 < x < 2 or x > 2

\frac{( x - 1 ) ( x + 4 )}{( x + 1 ) ( x - 5 )}

y = \frac{1}{1 - sin ( x )}

1.5 x^{2} - x + 3.7

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

f (x) = \frac{( x ^{2} - 9 )}{x + 4}

What is the domain of f(x)=(6x-x^2)/(x^2+4x-12) ?
The domain of f(x)=(6x-x^2)/(x^2+4x-12) is x<-6\lor-6<x<2\lor x>2