Question

If a function f is defined such that f(x+3) = f (x) + f(3) show that f(-3) = -f(3)

Answer 1

`Solution,\\f(x+3)=f(x)+f(3).......(1)\\Put~x=0~in~eq^n~(1),\\f(0+3)=f(0)+f(3)\\or, f(3)=f(0)+f(3)\\or, f(0)=0.........(2)\\Now,\\Put~x=-3~in~eq^n(1),\\f(-3+3)=f(-3)+f(3)\\or, f(0)=f(-3)+f(3)\\From~eq^n(2),\\0 = f(-3)+f(3)\\or, f(-3)=-f(3)~proved`