range

is the answer R = {n: n ε I - m² ; m ε W}

I=(-∞,∞) W=[1,∞)

that is i mean to say all integers except perfect squares!!!

Case I::

x≥0

suppose in the interval [n,n+1)

x² ε [n²,(n+1)²)

[x²] ε {n², n²+1, n²+2.....(n+1)²-1}

[x]=n

[x]²=n²

[x²]-[x]² ε {0,1,2,.....2n}

Case II:

x<0

x ε [-n,-(n-1))

x² ε ((n-1)²,n²]

[x²] ε {(n-1)²,(n-1)²+1...n²}

[x] = -n

[x]²=n²

[x²]-[x]²={-2n+1,-2n+2....0}

oops!!

seemingly now the range is coming R= I!! (ie -∞ to +∞ all integers!!!)

hey...it can never be R...

look thats because both the terms in the given function is an integer so the range can never be a non-ineger...

the best choice is what i got in second attempt...i.e. I

in the first attempt i was nt using any pen/paper and so got erronous results!!