Answer
Shown below.
Work Step by Step
Let us consider the function below:
$f\left( x \right)=\frac{3x-2}{5x-3}$
Now, to find the inverse of the above function
Put $y=f\left( x \right)$
So $y=\frac{3x-2}{5x-3}$
So, interchange y with x
$x=\frac{3y-2}{5y-3}$
Now solve for the value of y:
$\begin{align}
& 5xy-3x=3y-2 \\
& 5xy-3y=3x-2 \\
& y\left( 5x-3 \right)=3x-2 \\
& y=\frac{3x-2}{5x-3}
\end{align}$
Therefore,
${{f}^{-1}}\left( x \right)=\frac{3x-2}{5x-3}$
$\text{Since }f\left( x \right)={{f}^{-1}}\left( x \right)=\frac{3x-2}{5x-3}$. Therefore the function is its own inverse.
