question_answer 60)

      Show that the function  defined by  is one-one and onto function.  

Answer:

Given             Injective : Let x1 and x2 are two distinct elements of R.       Case ? I : When  and                                                                                                    Case-II : When             and             Case IV : When x1< 0 and x2                   and             Hence in all the above cases                   f is one-one.       Surjective : Let y be any element of R.          y = f(x)             (i)     When        y + xy = x             (ii)    When          y ? xy =x          y = xy + x                         Hence f is onto.