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

Question

If f(x) is an odd periodic function with period 2, then f(4) equals (A) 0 (B) 2 (C) 4 (D)  -4

Tardigrade Admin · Accepted Answer

Since, f(x) is odd periodic function with period 2. ∴ f(-x)=-f(x) and f(x+2)=f(x) ∴ f(2)=f(0) and f(-2)=f(-2+2)=f(0) Now, f(0)=f(-2)=-f(2)=-f(0) ∴ 2f(0)=0 ⇒ f(0)=0 ∴ f(4)=f(2)=f(0)=0

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

0

2

4

$- 4$

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

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

0

2

4

−4

Since, f(x) is odd periodic function with period 2. ∴ f(−x)=−f(x) and f(x+2)=f(x) ∴ f(2)=f(0) and f(−2)=f(−2+2)=f(0) Now, f(0)=f(−2)=−f(2)=−f(0) ∴ 2f(0)=0 ⇒ f(0)=0 ∴ f(4)=f(2)=f(0)=0

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

$- 4$

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