question_answer 74)

Let f : R  R be the signum functions defined as       and g : R  R be the Greatest Integer Function given by g(x) = [x], where [x] is greatest integer less than or equal to x. Then, does fog and gof coincide in (0, 1] ?  

Answer:

Given f : R  R and g : R  R defined as  and g(x) = [x]       (fog) (x) = f(g(x)) = f([x])                   and (fog) (x) = g(f(x))                   = [1] = 1             Clearly (fog) (x) and (gof) (x) does not coincide       .