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Question

If f(x)is an odd periodic function with period 2, then f(4) equals

A
2
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B
4
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C
-4
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Solution

We have, f(-x) = -f (x) and f(x+2) = f(x)
f(0) = f(0+2) = f (2)
Also f(0) = f(-2+2) = f (-2) = -f (2) = -f (0)
2f(0) = 0 f(0) = 0
Now, f(4) = f(2+2) = f (2) = f (2) = f(0+2) = f (0) = 0

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