Answer
Graph of $
f(x)=x^3-2
$ (blue) and $f^{-1}(x)$ (red, dashed)
Work Step by Step
Substituting the given values of $x$ in the given function, $
f(x)=x^3-2
$, results to
\begin{array}{c|c|c|c}
\text{If }x=-1: & \text{If }x=0 & \text{If }x=1 & \text{If }x=2
\\\\
f(x)=y=x^3-2 & f(x)=y=x^3-2 & f(x)=y=x^3-2 & f(x)=y=x^3-2
\\
y=(-1)^3-2 & y=0^3-2 & y=1^3-2 & y=2^3-2
\\
y=-1-2 & y=0-2 & y=1-2 & y=8-2
\\
y=-3 & y=-2 & y=-1 & y=6
.\end{array}
Tabulating the results above results to the table below.
\begin{array}{c|c}
\hline
x & f(x)
\\\hline
-1 & -3
\\\hline
0 & -2
\\\hline
1 & -1
\\\hline
2 & 6
\\\hline
\end{array}
Connecting the points $
(-1,-3),(0,-2), (1,-1) \text{ and } (2,6)
$ with a curve gives the graph of $
f(x)=x^3-2
$ (blue graph).
Interchanging the $x$ and $y$ coordinates of the points above gives the graph of the inverse function. That is, connecting the points $
(-3,-1),(-2,0), (-1,1) \text{ and } (6,2)
$ determines the graph of the inverse function (red dashed line).
