question_answer 41)

Let f :  be an invertible function. Show that the inverse of f?1 is f i.e. (f?1)?1 = f

Answer:

Given f :  be an invertible function        is both one-one and onto.       there exists a function  such that             Let y,  be such that                          is one-one,       Also, x = f?1(y) exists for        .       Hence f?1 is both one-one and onto.        exists.       Now              is the inverse of f?1.             which is proved.