Question

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

where [x] denotes the greatest integer function, then f is

(A) Continuous for every real x

(B) Discontinuous only at x = 0

(C) Discontinuous only at non-zero integral values of x

(D) Continuous only at x = 0

Answer 1

Answer is (A) Continuous for every real x

f(x) = [x]cos((2x - 1)/2)π = [x]cos(x - 1/2)π = [x]sinπx

f(x) = [x]sinπx, that is, f is continuous for every real x