[Math] Can you inverse a funcion by rotating it

Question

In school i sometimes run on some excercises where you need to calculate something that has an inverse function in it but you cannot find the inverse and you need to work your way around it. I know that the inverse function is symmetrical to the original one through the $y=x$, so i figured that if you rotate the function by 90 degrees positive turn (counter-clockwise) and then flip it through the $y$-axis you get the inverse. If you have a 1-1 function like $f(x)=e^x – e^{-x} + c$, is there a way to find the function that gives the same plot but rotated? I am not talking about simply rotating the graph, but about finding the funcion that gives the rotated plot.

Answer 1

if you rotate the [graph of a] function by $90$ degrees positive turn (counter-clockwise) and then flip it through the $y$-axis you get the [graph of the] inverse

That is correct. I wouldn't express it as "the same plot but rotated" because there is also that "flip", or reflection, that you did after rotating it.