已知,f(x)是R上的偶函数,且满足xf(x+1)=(x+1)f(x)则f(5/2)=
问题描述:
已知,f(x)是R上的偶函数,且满足xf(x+1)=(x+1)f(x)则f(5/2)=
答
令x = -1/2,则
-f(1/2)/2 = f(-1/2)/2
f(x)是R上的偶函数知f(-1/2) = f(1/2)
得到f(1/2) = 0
令x = 1/2,则f(3/2) = 0
令x = 3/2,则f(5/2) = 0