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Differential Calculus

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19 Jan 2012 11:06:01 IST

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tell whether function is even or odd

Mathematics

F(x)=(-1)^[x] is even,odd or neither of two (where [.] denotes the greatest function)

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pranjal shukla

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19 Jan 2012 18:23:12 IST

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neither the two.

ROHAN KUMAR

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19 Jan 2012 19:51:27 IST

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but ans is different

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19 Jan 2012 20:05:25 IST

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even is it write if so thn i vll tell my solution.

sambit kumar acharya

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19 Jan 2012 20:26:35 IST

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Even

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19 Jan 2012 20:34:56 IST

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Let me tell it..... F(x)+F(-x)=0... Use this simplify, i think it shud be EVEN

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19 Jan 2012 20:46:21 IST

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oh sorry ODD.... Quite confusd in evn or odd... Use the abov mode... It vll odd.

a.k.pavan kumar

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19 Jan 2012 20:56:25 IST

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odd.............................................. if f(x)=f(-x) then it is even but if f(x)=-f(x) then its odd

jagdish singh

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20 Jan 2012 09:08:09 IST

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$\hspace{-16}$(1)\;\;\; Here are two cases for $\mathbf{x}$\\\\ Either $\mathbf{x\in\mathbb{Z}}$ $O\mathbb{R}$ $\mathbf{x\notin\mathbb{Z}}$\\\\ $\bullet$ If $\mathbf{x\in\mathbb{Z}}$, Then $\mathbf{\left[-x\right]=-\left[x\right]}$\\\\ So $\mathbf{f(-x)=(-1)^{\left[-x\right]}=(-1)^{-\left[x\right]}=\frac{(-1)^\left[x\right]}{(-1)^{2\left[x\right]}}}$\\\\ So $\mathbf{f(-x)=(-1)^{\left[x\right]}=f(x)}$ (Even Function)\\\\ bcz $\mathbf{(-1)^{2\left[x\right]}=1}$\\\\ Similarly \\\\ $\bullet$ If $\mathbf{x\notin\mathbb{Z}}$, Then $\mathbf{\left[-x\right]=-\left[x\right]-1}$\\\\ So $\mathbf{f(-x)=(-1)^{\left[-x\right]}=(-1)^{-\left[x\right]-1}=-\frac{(-1)^\left[x\right]}{(-1)^{2\left[x\right]}}}$\\\\ So $\mathbf{f(-x)=-(-1)^{\left[x\right]}=-f(x)}$ (Odd Function)\\\\ bcz $\mathbf{(-1)^{2\left[x\right]}=1}$\\\\ So $\mathbf{f(x)=(-1)^{\left[x\right]}}$ is Even as well as Odd Function$

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20 Jan 2012 09:49:01 IST

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thanx fr correctin me.......

Manasi

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25 Jan 2012 01:07:53 IST

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