Question

f(x+4)=f(x)+f(4) then prove that f(0)=0 and f(-4)=-f(4)

Answer 1

Step-by-step explanation:

it is given that

: f(x+4). = f(x)+f(4)

: f(x+4) - f(4) = f(x)

: f(x) = f(x+4) - f(4) just reversed it

now

: f(0)=f(0+4) - f(4)

: f(0)=f(4) - f(4)

: f(0)=0 hence proved

now

:f(-4)=f(-4+4) - f(4)

:f(-4)=f(0) - f(4)

:f(-4)= 0 -f(4). because f(0)=0 is proved

f(-4)= - f(4) hence proved