What is the domain of sqrt((x^2-7)/(x^3-x^2-12x)) ?

The domain of sqrt((x^2-7)/(x^3-x^2-12x)) is -3 4

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domain of sqrt((x^2-7)/(x^3-x^2-12x))

domain

\frac{x ^{2} - 7}{x ^{3} - x ^{2} - 12 x}

- 3 < x \leq - 7 or 0 < x \leq 7 or x > 4

Interval Notation

(- 3, - 7] \cup (0, 7] \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

- 3 < x \leq - 7 or 0 < x \leq 7 or x > 4

Find undefined (singularity) points:

x = 0, x = - 3, x = 4

Combine real regions and undefined points for final function domain

- 3 < x \leq - 7 or 0 < x \leq 7 or x > 4

y = x^{2} + 4 x + 3

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

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

\frac{3}{2} x + 2 y = \frac{15}{2}, (- 4, 4)

7 x + 5 y = - 40

What is the domain of sqrt((x^2-7)/(x^3-x^2-12x)) ?
The domain of sqrt((x^2-7)/(x^3-x^2-12x)) is -3<x<=-sqrt(7)\lor 0<x<= sqrt(7)\lor x>4