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If f(x) is an odd periodic function with...

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

A

-4

B

4

C

2

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Since, f(x) is an odd periodic function with period 2.
`:." "f(-x)=-f(x)" and "f(x+2)=f(x)`
`:." "f(2)=f(0+2)=f(0)`
and `" "f(-2)=f(-2+2)=f(0)`
Now, `" "f(0)=f(-2)=-f(2)=-f(0)`
`implies" "2f(0)=0,i.e.,f(0)=0`
`:." "f(4)=f(2+2)=f(2)=f(0)=0`
Thus, `f(4)=0`
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