12th Class Mathematics Relations and Functions

  • question_answer 34)
    State with reason whether following functions have inverse. (i)     f : {1, 2, 3, 4}  {10} with       f = {(1, 10), (2, 10), (3, 10), (4, 10)} (ii)   g : {5, 6, 7, 8}  {1, 2, 3, 4} with       g = {(5, 4), (6, 3), (7, 4) (8, 2)} (iii)  h : {2, 3, 4, 5}  {7, 9, 11, 13} with       h : {(2, 7), (3, 9), (4, 11), (5, 13)}.  

    Answer:

    (i)   f : {1, 2, 3, 4} {10}       f(1) = 10, f(2) = 10, f(3) = 10, f(4) = 10              is not one-one. (i)     g : {5, 6, 7, 8}  {1, 2, 3, 4}             Here g(5) = 4 and g(7) = 4              for              is not one-one.       (iii)  h : {2, 3, 4, 5}  {7, 9, 11, 13}              = 7, h(3) = 9, h(4) = 11, h (5) = 13                          is one-one.       Also for every  there exists distinct value of x in {2, 3, 4, 5}        function ?h? is onto.       Hence function ?h? is invertible.        is given by        


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