What is the domain of g(x)=sqrt(6-1/(x^2)) ?

The domain of g(x)=sqrt(6-1/(x^2)) is x = 1/(sqrt(6))

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domain of g(x)=sqrt(6-1/(x^2))

domain

g (x) = 6 - \frac{1}{x ^{2}}

x \leq - \frac{1}{6} or x \geq \frac{1}{6}

Interval Notation

(- \infty, - \frac{1}{6}] \cup [\frac{1}{6}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{6} or x \geq \frac{1}{6}

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x \leq - \frac{1}{6} or x \geq \frac{1}{6}

f (x) = \frac{9}{x - 13} + \frac{3}{x - 2}

(x + 5) - (x^{2} + 8 x)

f (x) = \frac{( x + 4 )}{x ^{2} + 5 x}

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

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

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