Let Se be the set of all even functions in C(R): Se = {JEC(R) | VIER /(x) = /(-I)}. (a) Define, for each function / E C(R), the function fe: R - R by Se(x) = J(x) + / (-I) TER. 2 Show that fe E Se for each Je C(IR). (b) Define the function T: C(R) - C(R) by T(J) = Je. Show that T is a linear transfor- mation. (c) Find ker(7) and im(T)