What is the domain of sqrt(((x^2-x-6))/(x-4)) ?

The domain of sqrt(((x^2-x-6))/(x-4)) is -2 4

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domain of sqrt(((x^2-x-6))/(x-4))

domain

\frac{( x ^{2} - x - 6 )}{x - 4}

- 2 \leq x \leq 3 or x > 4

Interval Notation

[- 2, 3] \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 3 or x > 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

- 2 \leq x \leq 3 or x > 4

20 - x^{2}

f (x) = \frac{2 x - 4}{14 x ^{2} - 3 x - 5}

f (x) = \frac{2 x - 11}{2 x - 6}

f (x) = \frac{x ^{3} - 2 x + 4}{x - 3}

3 x - 3

What is the domain of sqrt(((x^2-x-6))/(x-4)) ?
The domain of sqrt(((x^2-x-6))/(x-4)) is -2<= x<= 3\lor x>4