Question

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

Answer 1

ANSWER
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)

∴f(4)=f(2+2)=f(2)=f(0)=0

Or

ANSWER
Given f(x) is an odd period function period function
→f(−x)=−f(x) and f(0)=0
since f(x) has period 2.
∴f(0)=f(2)=f(4)=0
Hence f(4)=0

Hope it helps you

Answer 2

Solution:- Given that f(x) is an odd function .

i.e f(-x) = -f(x)

Put x = 0

• ⟹F(0) = - f (0)
• ⟹ 2f(0) = 0
• ⟹ f(0) = 0

Also given function with period 2

∵ f(0) = 0

∴f(0) = f(0+2) =f(0+4) = f(0+6) ....... = 0

Since, f(4) = 0 Answer