For groups g_1 and g_2 a function f: g_1 -rightarrow g_2 is a homomorphism if f (g*1 h) = f(g) *2/(h) for every g, h e g1. let k = {g e g1 {(g) = e_2} where e_2 is the identity of g_2. show that k is a subgroup of g1. show that if f is one-to-one then k = {e1} and conversely that if k = {e1} then f must be one-to-one.