Answer
Graph of $
f(x)=-2x
$ (blue) and $f^{-1}(x)$ (red, dashed)
Work Step by Step
Let $y=f(x)$. Then the given function, $
f(x)=-2x
$ becomes
\begin{align*}\require{cancel}
y=-2x
.\end{align*}
By substituting values of $x$ and then solving the corresponding value of $y$, the graph can be determined. That is
\begin{array}{l|r}
\text{If }x=0: & \text{If }x=1
\\\\
y=-2x & y=-2x
\\
y=-2(0) & y=-2(1)
\\
y=0 & y=-2
.\end{array}
Hence, the points $
(0,0) \text{ and } (1,-2)
$ are on the given function. Connecting these points gives the graph of $
y=-2x
$ (blue graph).
Interchanging the $x$ and $y$ coordinates of the points above gives the graph of the inverse function. That is, connecting the points $
(0,0) \text{ and } (-2,1)
$ determines the graph of the inverse function (red dashed line).