Replace (f(x)) with (y)
Swap (x) and (y)
Solve the new equation for (y)
Replace (y) with (f^{-1}(x))
Check that (f(f^{-1}(x)) = x) and (f^{-1}(f(x)) = x)
Ensure the original function is one-to-one
Restrict the domain if needed
Verify the inverse is a function