已知函数f(x)满足f(x+y)+f(x-y)=2f(x)f(y),x和y都属于R,且f(0)≠0,试证明f(x)是偶函数
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已知函数f(x)满足f(x+y)+f(x-y)=2f(x)f(y),x和y都属于R,且f(0)≠0,试证明f(x)是偶函数
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)f(y),x和y都属于R,且f(0)≠0,试证明f(x)是偶函数
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)f(y),x和y都属于R,且f(0)≠0,试证明f(x)是偶函数
令x=y=0
故:f(0+0)+f(0-0)=2f(0)f(0)
即:2f(0)=2 f(0)f(0)
因为f(0)≠0
故:f(0)=1
令x=0
故:f(y)+f(-y)=2f(0)f(y)
故:f(y)+f(-y)=2f(y)
故:f(-y)=f(y)
因为y任意
故:f(-x)=f(x)
故:f(x)是偶函数(定义域R关于原点对称)
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