M2 1條

火中有火

-終場ソ使者-

We first consider the value of f(0).
Assume b=0,
f(a+0)+f(a-0)=2(f(a)+f(0))
f(a)+f(a)=2f(a)+2f(0)
f(0)=0,
assume a=0
f(0+b)+f(0-b)=2(f(0)+f(b))
f(b)+f(-b)=2f(0)+2f(b)
f(b)+f(-b)=2f(b)    (since f(0)=0)
f(-b)=f(b)
therefore, f(x) is an even function

火中有火