The functions \(f\) and \(g\) are defined on the entire number line and are reciprocal. It is known that \(f\) is represented as a sum of a linear and a periodic function: \(f (x) = kx + h (x)\), where \(k\) is a number, and \(h\) is a periodic function. Prove that \(g\) is also represented in this form.