Question

if f(x+3)=f(x)+f(3) then prove that
(a) f(0) =0 (b) f(-3)=-f(3)
(c) f(6) + 2f(-3)=0

Answer 1

if f(x+3)=f(x)+f(3)

then,

(a) f(0)=0

L.H.S.=f(0)= f*0 =0

R.H.S.= 0

… hence, L.H.S.=R.H.S prooved

(b) f(―3)= -f(3)

L.H.S.= f(-3)=f*-3=-f(3)

R.H.S.= -f(3)

… hence, L.H.S. =R.H.S. prooved

(c) f(6)+2f(-3)=0

L.H.S.= f*6+(-6f)= 6f-6f =0

R.H.S.=0

… hence, L.H.S. =R.H.S. prooved

hope it will help you