Question

If f(x + 2) = f(x) + f(2) then prove that: f(0) = 0 and f(-2) = -f(2)

Answer 1

f(0)=0,

f(-2)=-f(2)

Explanation:

f(x+2)=f(x)+f(2)

1. x=0

f(0+2)=f(0)+f(2)

f(2)=f(0)+f(2)

f(0)=f(2)-f(2)=0

f(0)=0

2. x=-2

f(-2+2)=f(-2)+f(2)

f(0)=f(-2)+f(2)

f(0)=0, f(-2)+f(2)=0

f(-2)=-f(2)