Replace (f(x)) with (y)
Write the equation (y = f(x))
Swap (x) and (y) to get (x = f(y))
Solve the new equation for (y)
Replace (y) with (f^{-1}(x))
Check that composing gives the identity on the domain (where defined): (f(f^{-1}(x)) = x) and (f^{-1}(f(x)) = x)
Restrict the original function’s domain if needed to make it one-to-one before finding (f^{-1})