Question

. If f(x+8)=f(x)+f(8) then prove that: f(0)=0 and f(-8)=-f(8). ​

Answer 1

Explanation:

Given

The equation is
`f(x+8)=f(x)+f(8)`

Substitute 0 for x

`\Rightarrow f(0+8)=f(0)+f(8)\\\Rightarrow f(0)=f(8)-f(8)\\\Rightarrow f(0)=0`

Now, substitute
`-8` for
`x`

`\Rightarrow f(-8+8)=f(-8)+f(8)\\\Rightarrow f(0)=f(-8)+f(8)\\\Rightarrow 0=f(-8)+f(8)\\\Rightarrow f(-8)=-f(8)`

Hence proved