Three functions are written on the board: \(f_1 (x) = x + 1/x\), \(f_2 (x) = x^2, f_3 (x) = (x - 1)^2\). You can add, subtract and multiply these functions (and you can square, cube, etc. them). You can also multiply them by an arbitrary number, add an arbitrary number to them, and also do these operations with the resulting expressions. Therefore, try to get the function \(1/x\).
Prove that if you erase any of the functions \(f_1, f_2, f_3\) from the board, it is impossible to get \(1/x\).