#### Answer

See image

#### Work Step by Step

The graphs of $f$ and $f^{-1}$ (if the inverse is defined)
are symmetrical about the line $y=x.$
Symmetry:
Reflection of the point (a,b) about the line $y=x$ is the point (b,a).
The graph of $f(x)=x^{3}+1$ passes the horizontal line test,
(as in example 8, the graph of $y=x^{3}$ is raised up by 1 unit)
so $f^{-1}(x)$ exists.
Graph $f$ by creating a table of function values:
$\left[\begin{array}{lllllll}
x & -2 & -1 & 0 & 1 & 2 & \\
y=f(x) & -7 & 0 & 1 & 2 & 9 &
\end{array}\right]$
Join the points with a smooth curve (blue graph).
To graph $f^{-1}(x) $we plot the points $(y,x)$ from the above table.
Join the points with a smooth curve (red graph)