What is the domain of f(x)=(sqrt(x+3))/(x^2-x-12) ?

The domain of f(x)=(sqrt(x+3))/(x^2-x-12) is -3 4

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domain of f(x)=(sqrt(x+3))/(x^2-x-12)

domain

f (x) = \frac{x + 3}{x ^{2} - x - 12}

- 3 < x < 4 or x > 4

Interval Notation

(- 3, 4) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 3

Find undefined (singularity) points:

x = 4, x = - 3

Combine real regions and undefined points for final function domain

- 3 < x < 4 or x > 4

f (x) = x + 2

\frac{11}{x}

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

f (x) = 2 lo g_{3} (- x + 8) - 1

\frac{4 x - 6}{- x + 2}

What is the domain of f(x)=(sqrt(x+3))/(x^2-x-12) ?
The domain of f(x)=(sqrt(x+3))/(x^2-x-12) is -3<x<4\lor x>4