Think twice
Number of integers in the range of the function:
if can have all real values except 0 is:
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1 solution
f(x) = x 3 + 2 x 2 + 2 x + 1 x + 1 + 1
So,
f(x) = x 2 + x + 1 1 + 1
Maximum value of the expression above is obtained when x 2 + x + 1 1 is maximum and vice- versa
Hence the range of f is ( 1 , 7 / 3 ]
Only Integer in this range is : 2
However , 2 cannot be achieved as it will be achieved only at x = 0 which is not in the domain of f.