One may check involutivity: of course, x * x − f *(x *) is always bounded as a function of x *∈{ c }, hence I ** = R. Then, for all x one has sup x ∗ ∗ ∈ ∈ { c } ( x x ∗ ∗ − − f ∗ ∗ ( x ∗ ∗ ) ) = x c , and hence f **(x) = cx = f (x).