What is the equation of the curve, h(x) oscillating between f(x) and g(x)? In other words, h(x) = f(x) for even integral values of x and h(x) = g(x) for odd integral values of x? The values of h(x) for non-integral x are on the oscillatory curve shown.
Actually, curves such as this, are important in analog communication theory. The amplitude modulation (AM) wave is actually special case of this curve.