Inverse of $y=1/x$ Can anybody say anything about the inverse function of $y=1/x$ and plot it on a graph and then compare the graphs of the given function and it's inverse? Is $y=1/x$ invertible? If yes then do the graphs of $y=1/x$ and its inverse coincide?

To get an inverse function you need to interchange $x$ and $y$ so here.. the relation  remains unchanged, the equiangular hyperbola remains its own inverse.
For an implicit relation
$$ x^2 + y^2= \sin xy $$
the inverse function also coincides with the first function.
Graph of these functions appear as mirror images with respect to line $x=y$
As an exercise try to find the inverse function
$$ y= \pm \sqrt {(x+1)(3-x)} +1 $$
considering both signs of $\pm$ which also reflect about the line $x=y$ two parts of a circle of radius 2.
