What is the domain of (x^2-11)/(sqrt(36x^2-6x-6)) ?

The domain of (x^2-11)/(sqrt(36x^2-6x-6)) is x 1/2

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domain of (x^2-11)/(sqrt(36x^2-6x-6))

domain

\frac{x ^{2} - 11}{36 x ^{2} - 6 x - 6}

x < - \frac{1}{3} or x > \frac{1}{2}

Interval Notation

(- \infty, - \frac{1}{3}) \cup (\frac{1}{2}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{3} or x \geq \frac{1}{2}

Find undefined (singularity) points:

x = \frac{1}{2}, x = - \frac{1}{3}

Combine real regions and undefined points for final function domain

x < - \frac{1}{3} or x > \frac{1}{2}

y = 9 - x^{2} + 3

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

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

f (x) = \frac{1 + x ^{4}}{x ^{2} - x ^{4}}

f (x) = - e^{x - 2}

What is the domain of (x^2-11)/(sqrt(36x^2-6x-6)) ?
The domain of (x^2-11)/(sqrt(36x^2-6x-6)) is x<-1/3 \lor x> 1/2