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Which of the following function/function...

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

Text Solution

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The correct Answer is:
a,b,c
(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.
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