If f: R → R is a function defined by f(x) = [x] cos((2x - 1)/2)π

• Limits Continuity

If f: R → R is a function defined by f(x) = [x] cos((2x - 1)/2)π, where [x] denotes the greatest integer function, then f is

1. discontinuous only at x = 0
2. discontinuous only at non-zero integral values of x
3. continuous only at x = 0
4. continuous for every real x

Answer

f(x) = [x]cos((2x - 1)/2)π

= [x]cos(x - 1/2)π

= [x] sin π x

The correct option is D.