Answer
Graph of $f(x)=2x-1$ (blue) and $f^{-1}(x)$ (red, dashed)
Work Step by Step
Let $y=f(x)$. Then the given function, $
f(x)=2x-1
$ becomes
\begin{align*}\require{cancel}
y=2x-1
.\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-1 & y=2x-1
\\
y=2(0)-1 & y=2(1)-1
\\
y=0-1 & y=2-1
\\
y=-1 & y=1
.\end{array}
Hence, the points $
(0,-1) \text{ and } (1,1)
$ are on the given function. Connecting these points gives the graph of $
f(x)=2x-1
$ (blue graph).
Interchanging the $x$ and $y$ coordinates of the points above gives the graph of the inverse function. That is, connecting the points $
(-1,0) \text{ and } (1,1)
$ determines the graph of the inverse function (red dashed line).
