Let    fx=sec-11+cos2x, where [.] denotes the greatest integer function. Then the

fx=sec-11+cos2x        fx  is  defined   if  1+cos2x≤-1   or   1+cos2x≥1k.e.,        cos2x≤-2not  possible  or   cos2x≥0i.e.,        cos2≥0   or  x∈RNow,   0≤cos2x≤1   or   1≤1+cos2x≤2or        1+cos2x=1,2or        sec-11+cos2x=sec-11,sec-12Hence,   the   range   is  sec-11,sec-12.