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​Q55. Let (x) =  x 2 - 4 x 2   + 4 , for | x |  > 2, then the function  f : (–  , –2] ∪ [2,  (–1, 1) is :

         (a) one-one into                                    (b) one-one onto

    ​     (c) many-one into                                 (d) many- one onto 


Q56. The function   (x) = sin log (x +  x 2   + 1 ) is :
           (a) even function

           (b) odd function

           (c) neither  even nor odd

           (d) periodic function
 
 

Dear student
56.
We have,fx=sinlogx+1+x2Consider, f-x=sinlog-x+1+-x2=sinlog-x+1+x2×1+x2+x1+x2+x=sinlog1+x22-x21+x2+x=sinlog1+x2-x21+x2+x   using a2-b2=a+ba-b=sinlog11+x2+x=sinlog1+x2+x-1=sin-log1+x2+x    using logmn=nlogm=-sinlog1+x2+x   using sin-x=-sinx=-fxi.e. f-x=-fxSo, f is an odd function.
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