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

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

JamiaJamia 2008

Solution:

Since, $ f(x) $ is odd periodic function with period 2. $ \therefore $ $ f(-x)=-f(x) $ and $ f(x+2)=f(x) $ $ \therefore $ $ f(2)=f(0) $ and $ f(-2)=f(-2+2)=f(0) $ Now, $ f(0)=f(-2)=-f(2)=-f(0) $ $ \therefore $ $ 2f(0)=0 $ $ \Rightarrow $ $ f(0)=0 $ $ \therefore $ $ f(4)=f(2)=f(0)=0 $