f(x+y)+f(x-y)=2f(x)乘f(y) ,且f(x)不等于0,求f(1)
f(x+y)+f(x-y)=2f(x)乘f(y) ,且f(x)不等于0,求f(1)
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數(shù)學(xué)人氣：309 ℃時間：2020-05-26 05:33:03
優(yōu)質(zhì)解答
f(x+y)+f(x-y)=2f(x)f(y)令y=x,得：f(2x)+f(0)=2f(x)f(x)令y=-x,得：f(0)+f(2x)=2f(x)f(-x)兩式對比,可知：f(x)=f(-x)所以,f(x)是偶函數(shù).令y=0,得：f(x)+f(x)=2f(x)f(0)因?yàn)閒(x)不等于0,所以：f(0)=1只能求出這些了....
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