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

lo g_{e} (x^{2} + 2 \cdot x - 1 + 1)

f (x) = \frac{x + 1}{x ^{2} - 2 x - 3}

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

f (x) = \frac{1}{3} x^{3} + \frac{2}{5} x + 1

ln (3 x + 12)

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