If f(x) is odd periodic function with period 1 then f(2) is equal… - Vidyadip

MCQ

If $f(x) $ is odd periodic function with period $1 $ then $ f(2)$ is equal to

✓
$0$
B
$1$
C
$-1$
D
can't obtain

✓

Answer

Correct option: A.

$0$

a
since $f(x)$ is an odd periodic function with period 2

$\therefore f(x)=-f(x)$ and $f(x+2)=f(x)$

$\therefore f(2)=f(0+2)=f(0)$

and $f(-2)=f(-2+2)=f(0)$

Now $f(0)=f(-2)=-f(2)=-f(0)$

$\therefore f(4)=f(2+2)=f(2)=f(0)=0$

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