please be thorough and explain and every step

3. (a) Let R be a ring, not necessarily commutative or unital. A function f : R - R is R-linear if f(x +y) = f(x) + f(y) and f(x . r) = f(x) . r for all r, x, y E R. Show that the set of R-linear functions is not a subring of R" with pointwise addition and multiplication. (b) However, show that the set of linear functions is a ring with pointwise addition but with composition as the multiplication. (c) Show that if R is unital, then the ring of R-linear functions R - R is isomorphic to R. (d) Show that the ring of linear functions R - R is always unital. In particular, it is not isomorphic to R if R is not unital