1it is discontinuous....i don't think it is even and i think its period cannot be defined
How do you prove that (sgn{x})sgn{x} is even, periodic and discontinuous?
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10 Answers
1chant this mantra 500 times
*om proovaya namah*om evenaya namah*om periodicaya namah*om discontinuosaya namah* and u r done[1]
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39sgn{x} will always be either 0 or 1, isn't it? {x} gives values 0 ≤ x < 1 and the signum function gives -1 if input is negative, 0 if 0, +1 if input is positive.
Hence sgn{x} will always be either 0 or 1. It will be 0 only when {x} = 0, that is, when x is an integer.
(sgn{x})sgn{x} will be 00 when x is an integer...it will keep oscillating between integral points, looks to me.
1@ Pritish -
Yes I got that it is discontinuous.
The function is periodic as it oscillates between 1 and 0 at integral and non integral points.
What about the function being even?
39I guess we have to define the function at certain points to find whether it is even or odd....that is -:
1. When x is 0.
2. When x is integral.
3. When x is non-integral.
Positive and negative values of x hardly matter...{x} will always yield a non-negative result.