Can someone help me with the question below and explain it with steps? It is not part of any work I have to submit ("not to turn in") and is a problem I am attempting as part of revision. Thanks!

2. (Not to turn in) (a) Suppose T : R - R is a linear transformation, show there exists B ER such that for all x E R, T(x) = Bx. (b) Suppose T : R - R satisfies for all x, y ER, T(xty) = T(x) + T(y) and T is continuous, show there exists B E R such that T(x) = x. (c) Show there exists T : R - R satisfies for all x, y E R, T(a ty) = T(x) + T(y) which is not of the form T(x) = Bx