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Question

If f(x)is an odd periodic function with period 2, then f(4) equals
  1. 0
  2. 2
  3. 4
  4. -4


Solution

The correct option is A 0
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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