Which of the following function/functions is/are periodic ?
(a) `sgn(e^(-x)) " (b) " sinx + |sinx|`
(c ) `min(sinx, |x|) " (d) " (x)/(x)`

Answer

a,b,c

Explanation

(a) `f(x) = sgn (e^(-x))=1 " as " e^(-x) gt 0 AA x in R`.
Therefore, `f(x)` is periodic function.
(b) `g(x)=sinx +|sin x|` is periodic with period `2pi` as
`f(x+2pi)=f(x).`
(c ) `h(x) = min(sinx, |x|)=sinx,` which is periodic.
(d) `p(x)=(x)/(x)=1, x ne 0, ` which is nonperiodic.