设f(x)的定义域为（-∞,+∞）,且对任何X,Y都有f(x+y)+f(x-y)=2f(x)f(y),且f(x)≠0,证明f(x)为偶函数.
人气：111 ℃ 时间：2019-10-23 04:44:50
解答
令y=x有：f(2x)+f(0)=2f(x)f(x)
令y=-x有：f(0)+f(2x)=2f(x)f(-x)
由此得2f(x)f(x)=2f(x)f(-x)
因f(x)≠0,故f(x)=f(-x) 即f(x)为偶函数
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