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

Solution:    Given that      $f(-x)=-f(x)$        $.......(1)$

And                  $f(x+2)=f(x)$              $.......(2)$

From  $(2)$ ,     $f(-2)=f(2)=f(0)$      $........(3)$

From   $(1)$,     $f(-2)=f(0)=-f(0).$

$\Rightarrow$                     $2f(0)=0$   $\Rightarrow$    $f(0)=0$

$\Rightarrow$                     $f(4)=f(2)=f(0)=0.$

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
##### Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout NEET (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-