If F open parentheses x close parentheses equals fraction numerator sin space pi open square brackets x close square brackets over denominator open curly brackets x close curly brackets end fraction, then F(x) is: (where {.} denotes fractional part function and [..] denotes greatest integer function and sgn (x) is a signum function)

(A) periodic with fundamental period 1
(B) even
(C) range is singleton
(D) identical to sgn open parentheses sgn fraction numerator open curly brackets x close curly brackets over denominator square root of open curly brackets x close curly brackets end root end fraction close parentheses minus 1

Dear Student,
Please find below the solution to the asked query:

Fx=sinπxxAs fractional part is 0 for xI, hence domain of fx=R-INow x always gives integer and at integral multiple of π, sine is 0, henceFx=0 for xR-IHence range of Fx is 0-a singleton set...OptionC

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.

  • 2
u have given thw ans XD!
  • -5
try yourself
  • -5
What are you looking for?