Most Important Selected Qs for JEE AdvancedMathematicsFunctions
Which of the following function is periodic?
Options
- Af(x)= sgn (e^ -x ) where sgn x denotes signum function of x .
- Bf(x)= x+| x|
- Cf(x)= .( x,|x|)
- Df(x)= [x+ 1 2 ]+ [x- 1 2 ]+2[-x] where [x] denotes greatest integer less than or equal to x .
Correct answer
D. f(x)= [x+ 1 2 ]+ [x- 1 2 ]+2[-x] where [x] denotes greatest integer less than or equal to x .
Step-by-step solution
aligned & (A) f(x)= sgn (e^ -x )=1 x R & f(x) is periodic. aligned (As constant function is periodic function.) (B) f(x)= x+| x| . Clearly f(x) is periodic with fundamental period which is L.C.M. of 2 and i.e. 2 . (C) As x |x| x R Clearly f(x)= x Hence f(x)= .( x|x|)= x f(x) is periodic. (D) f(x)= (x+ 1 2 )- x+ 1 2 + (x- 1 2 )- x- 1 2 +2((-x)- x ) d f(x)=- x+ 1 2 - x- 1 2 -2 x Clearly f(x) is periodic with fundamental period 1