[′kän·jə·gət ′kän‚veks ′fəŋk·shənz] (mathematics) Two functions ƒ(x) and g (y) are conjugate convex functions if the derivative of ƒ(x) is 0 for x = 0 and constantly increasing for x > 0, and the derivative of g (y) is the inverse of the derivative of ƒ(x).