The period of f(x)=esin{x}+sin(π2[x]) is ([.] and {.} are the greatest integer function and fraction function)

esin{x} period =1sin(π2[x]) [x]=2k k∈Zsin(π2[x])=0 [x]=2k+1sin(π2[x])=±1Not periodic

The period of f(x)=esin{x}+sin(π2[x]) is ([.] and {.} are the greatest integer function and fraction function)

esin{x} period =1sin(π2[x]) [x]=2k k∈Zsin(π2[x])=0 [x]=2k+1sin(π2[x])=±1Not periodic

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The period of $f (x) = e^{\sin {x}} + \sin (\frac{π}{2} [x])$ is ( $[.]$ and ${.}$ are the greatest integer function and fraction function)

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Not periodic

answer is D.

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Detailed Solution

$e^{\sin {x}}$ period $= 1$

$\sin (\frac{π}{2} [x]) [x] = 2 k k \in Z$

$\sin (\frac{π}{2} [x]) = 0 [x] = 2 k + 1$

$\sin (\frac{π}{2} [x]) = \pm 1$

Not periodic

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The period of f(x)=esin{x}+sin(π2[x]) is ([.] and {.} are the greatest integer function and fraction function)

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The period of $f (x) = e^{\sin {x}} + \sin (\frac{π}{2} [x])$ is ( $[.]$ and ${.}$ are the greatest integer function and fraction function)