Answer
(a) See the image below.
(b) Yes, the graph clearly shows that $f$ and $f^{-1}$ are the same function.
(c) $f^{-1}(x)=\frac{x+3}{x-1}$
Work Step by Step
(a) See the image above.
(b) Due to the definition of the inverse function, we know that the graph of an inverse function is a reflection of a graph about $y=x$ axis.
As we can clearly see from the image above, the graph is symmetrically divided by $y=x$ axis. So, yes $f$ and $f^{-1}$ are the same function.
(c) To calculate the inverse function, we will do the following:
$f(x)=\frac{x+3}{x-1}$
First we have to write it down in terms of $y$ and $x$:
$y=\frac{x+3}{x-1}$
Then replace $y$ by $x$ and vice versa:
$x=\frac{y+3}{y-1}$
And at last solve it for $y$
$x(y-1)=y+3$
$xy-x=y+3$
$xy-y=x+3$
$y(x-1)=x+3$
$y=\frac{x+3}{x-1}$
$f^{-1}(x)=\frac{x+3}{x-1}$