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

We save the definition:

f (x) = \frac{\sqrt[3]{x - 3}}{x^{3} - 3}

Let's evaluate the domain of

\frac{\sqrt[3]{x - 3}}{x^{3} - 3}

For the expression

\frac{\sqrt[3]{x - 3}}{x^{3} - 3}

to be defined, we must have:

x^{3} - 3 \neq 0

The power being odd,

x^{3} = 3

has a single real solution,

\sqrt[3]{3}

▶Domain of definition:

x \neq \sqrt[3]{3}

The numeric value of:

x \neq \sqrt[3]{3}

is:

▷

x \neq 1.4422 (approximate value)