Help me with this homework please, and explain the answer..

2.7 Determine which of the following are linear operators, and which are not. (a) The parity operator [f (x)] = f(-x). (b) The translation operator T[f (x)] = f(x + 1). (c) The operator LIf (x)] = f(x) + 1. 2.8 Consider the identity operator /, defined by I If (x)] = f(x). (a) Show that / is a linear operator. (b) Find the eigenfunctions and corresponding eigenvalues of