Properties of Greatest Integer Function (ix) `[x]ltk implies xltk; where k epsilon Z` (x)`[x+y]=[x]+[y+x-[x]]` for all `x;yepsilon R`

Properties of Greatest Integer Function (ix) [x]

Properties of Greatest Integer Function (vi)[x]>=k rArr x>=k; whereke Z(vii)[x] k rArr x>(k+1) ; where k varepsilon Z

Properties of smallest integer function property (i)[-n]=-[n]where n epsilon N (ii) [-x]=-[x]+1; where xepsilon R-Z (iii) [x+n]=[x]+n where x epsilon R-Z and n epsilon Z (iv) [x]+[-x]={1; x notinZ ; 0 ; xinZ} (v) [x]-[-x]={2[x]-1; xnotinZ ; 2[x] ; if xinZ

Let f(x)=[x]cos ((pi)/([x+2])) where [ ] denotes the greatest integer function. Then, the domain of f is (a) x epsilon R, x not an integer (b) x epsilon (-oo, -2)uu[-1,oo) (c) x epsilon R, x!=-2 (d) x epsilon (-oo,-1]

Find all the points of discontinuity of the greatest integer function defined by f(x) = [x] where [x] denotes the greatest integer less than or equal to x.

Find all the points of discontinuity of the greatest integer function defined by f(x) = [x] , where [x] denotes the greatest integer less than or equal to x.