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未打問題都唔該定版主/答的人先...
岩岩入黎個版真係10條數有7~8條比版主KO
可惜我問的都好似好低LV咁

Let y=f(x) be a function such that for any real numbers a and b,
   f(a+b)+f(a-b)=2(f(a)+f(b)). Prove that f(x) is an even function.

-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

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( ...
-終場ソ使者- 發表於 7-8-2011 20:06

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