How do you find the inverse of #f(x)=1/(2x)#?
Our inverse will be a function y = g(x) such that f(g(x)) = x
If we can manipulate our initial function so that, instead of y = some function of x, we have x = some function of y, we'll have our inverse.
...which is your inverse function. It's traditional to swap the variables, so, our inverse function is
...so this function is its own inverse!
We'll check our work. Subtitute our inverse function definition into our original equation, and calculate f(g(x)). We should get back x.