The domain of x3·cotx is

R − { x / x = n π , n ∈ Z }

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The domain of $\sqrt[3]{x} \cdot c o t x$ is

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$R - {x / x = n π, n \in Z}$

$R$

$R - \{0\}$

$R^{+}$

answer is C.

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The given function is $\sqrt[3]{x} \cdot c o t x$

In the above funciton $\sqrt[3]{x}$ has no restriction

but $c o t x = \frac{\cos x}{\sin x}$ , and $\sin x$ is not defined at multiples of $π$

Hence, The domain of the function $\sqrt[3]{x} \cdot c o t x$ is $R - {x / x = n π, n \in Z}$

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