If `f(x)` is an odd function, `f(1)=3,f(x+2)=f(x)+f(2),` then the value of `f(3)` is________

Answer

9

Explanation

Given `f(x+2)=f(x)+f(2)`
Put `x=-1.` Then
`f(1)=f(-1)+f(2)`
`or f(1)= -f(1) +f(2)`[as `f(x)` is an odd function]
`or f(2)=2f(1)=6`
Now, put `x=1`.
We have `f(3)=f(1)+f(2)=3+6=9.`