In this paper a notion of difference function Δ f is introduced for real-valued, non-negative and log-concave functions f defined in R n . The difference function represents a functional analogue of the difference body K + (− K ) of a convex body K. The main result is a sharp inequality which bounds the integral of Δ f from above in terms of the integral of f . Equality conditions are characterized. The investigation is extended to an analogous notion of difference function for α -concave functions, with α α -difference function of f in terms of the integral of f is proved. The bound is sharp in the case α = −∞ and in the one-dimensional case.