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

The domain of f(x)=(sqrt(x^2-x-6))/(x^2-x-2) is x = 3

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domain of f(x)=(sqrt(x^2-x-6))/(x^2-x-2)

domain

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

x \leq - 2 or x \geq 3

Interval Notation

(- \infty, - 2] \cup [3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x \geq 3

Find undefined (singularity) points:

x = 2, x = - 1

Combine real regions and undefined points for final function domain

x \leq - 2 or x \geq 3

f (t) = \frac{1}{t}

e^{a r c s i n (x)}

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

f (x) = - 2 x + 12

f (x) = 4 x - 1

What is the domain of f(x)=(sqrt(x^2-x-6))/(x^2-x-2) ?
The domain of f(x)=(sqrt(x^2-x-6))/(x^2-x-2) is x<=-2\lor x>= 3