We define the first difference f of a function f (x) by f (x) = f (x + 1) f (x). 37. Show that

We define the first difference δf of a function f (x) by δf (x) = f (x + 1) − f (x).
37. Show that if f (x) = x2, then δf (x) = 2x + 1. Calculate δf for f (x) = x and f (x) = x3.
39. Show that for any two functions f and g, δ(f + g) = δf + δg and δ(cf ) = cδ(f ), where c is any constant.