Answer
$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $x\neq y$ and $y\neq x^{3}$ $\}$
Work Step by Step
f is defined for points (x,y) that do not yield zero in the denominator.
We exclude all points for which $\left\{\begin{array}{l}
y=x\\
y=x^{3}
\end{array}\right.$
We graph the line and the cubic curve with dashed lines.
Domain: all points not lying on either of the graphs of $\left\{\begin{array}{l}
y=x\\
y=x^{3}
\end{array}\right.$.
or, in set notation, $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $x\neq y$ and $y\neq x^{3}$ $\}$
