What is the domain of f(x)=-sqrt(1/(x^2-81)) ?

The domain of f(x)=-sqrt(1/(x^2-81)) is x 9

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domain of f(x)=-sqrt(1/(x^2-81))

domain

f (x) = - \frac{1}{x ^{2} - 81}

x < - 9 or x > 9

Interval Notation

(- \infty, - 9) \cup (9, \infty)

Solution steps

Find non-negative values for radicals:

x < - 9 or x > 9

Find undefined (singularity) points:

x = 9, x = - 9

Combine real regions and undefined points for final function domain

x < - 9 or x > 9

What is the domain of f(x)=-sqrt(1/(x^2-81)) ?
The domain of f(x)=-sqrt(1/(x^2-81)) is x<-9\lor x>9