The range of fx=x+1x+2x+3x+4+5 for x∈-6,6 is

Let   gx=x+1x+2x+3x+4The rough graph of g(x) is given as follows:∴  gx=x+1x+2x+3x+4                =x+1x+4x+2x+3                =x2+5x+4x2+5x+6                =tt+2=t+12-1                wheret=x2+5x+4Now,gmin=-1,  for  which  x2+5x+4=-1  has  real   roots   in  -6,6.Also,    g6=7×8×9×10=5040.Hence, the range of gx  is  -1,5040  for  x∈-6,6.Then, the range of f(x) is [4, 5045].