Step-by-step explanation:
Given
The equation is [tex]f(x+8)=f(x)+f(8)[/tex]
Substitute 0 for x
[tex]\Rightarrow f(0+8)=f(0)+f(8)\\\Rightarrow f(0)=f(8)-f(8)\\\Rightarrow f(0)=0[/tex]
Now, substitute [tex]-8[/tex] for [tex]x[/tex]
[tex]\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)[/tex]
Hence proved
