Question

Why does it not make sense to graph f and f−1 on the same set of axes?

Answer 1

Here you have two graphs, one -- graph of the function y=f(x) on the coordinate plane with axes x and y, another -- graph of the function
`x=f^(-1)(y)` on the coordinate plane with axes y and x.

Actually, these graphs are graphs of the same function, only axes are changed.

It makes the sense to graph to functions
`f(x)` and
`f^(-1)(x)` on the same set of axes, not graphs of the same function
`y=f(x)` and
`x=f^(-1)(y)` on the different set of axes.