Question

If [x} denotes the greatest integer £ x, then range of the function f(x) = [x2 + x + 1] is

Answer 1

the range of any function is (minimum value to maximum value)
the range of [x] is all integer between minus infinity to plus infinity
so range of y = [ x^2 + x + 1]  
                    =[ (x + 1/2)^2 + 3/4]       { (x + 1/2 )^2 +3/4 >0 for all value of x }
so minimum value of (x+1/2)^2 +3/4  is 3/4 and [3/4] = 0
 so range of y = 0,1,2,3,4,5...............  (all non negative integer)