Replace (f(x)) with (y)
Swap (x) and (y)
Solve for (y)
Replace (y) with (f^{-1}(x))
Verify by checking (f(f^{-1}(x)) = x) and (f^{-1}(f(x)) = x)
Ensure the original function is one-to-one
Restrict the domain if necessary
Use algebraic manipulation to isolate the inverse variable
For a graph, reflect the function across the line (y = x)