What is the domain of f(x)= 1/(\sqrt[4]{x^2-8)} ?

The domain of f(x)= 1/(\sqrt[4]{x^2-8)} is x 2sqrt(2)

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domain of f(x)= 1/(\sqrt[4]{x^2-8)}

domain

x < - 22 or x > 22

Interval Notation

(- \infty, - 22) \cup (22, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 22 or x \geq 22

Find undefined (singularity) points:

x = 22, x = - 22

Combine real regions and undefined points for final function domain

x < - 22 or x > 22

What is the domain of f(x)= 1/(\sqrt[4]{x^2-8)} ?
The domain of f(x)= 1/(\sqrt[4]{x^2-8)} is x<-2sqrt(2)\lor x>2sqrt(2)