What is the domain of f(x)=\sqrt[3]{x/(x^3-8)} ?

The domain of f(x)=\sqrt[3]{x/(x^3-8)} is x 2

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domain of f(x)=\sqrt[3]{x/(x^3-8)}

domain

x < 2 or x > 2

Interval Notation

(- \infty, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 2

The function domain

x < 2 or x > 2

f (x) = x^{2} - 8 x + 3

x^{2} - 18 x + 81

f (x) = - 7 - x

f (x) = 5 e^{- x}

f (x) = (2 x - 3) (x^{2} + 8 x + 16)

What is the domain of f(x)=\sqrt[3]{x/(x^3-8)} ?
The domain of f(x)=\sqrt[3]{x/(x^3-8)} is x<2\lor x>2