who are you help me to solve the math problem?已知函数f(x)是定义在实数集R上的不恒为零的偶函数,且对任何实数x都有xf(x+1)=(1+x)f(x),则f(5/2)的值是多少?（要详细答案）

来源：学生作业帮助网编辑：作业帮时间：2024/05/04 04:07:47

$who are you help me to solve the math problem?已知函数f(x)是定义在实数集R上的不恒为零的偶函数,且对任何实数x都有xf(x+1)=(1+x)f(x),则f(5/2)的值是多少?（要详细答案）$

who are you help me to solve the math problem?已知函数f(x)是定义在实数集R上的不恒为零的偶函数,且对任何实数x都有xf(x+1)=(1+x)f(x),则f(5/2)的值是多少?（要详细答案）
who are you help me to solve the math problem?
已知函数f(x)是定义在实数集R上的不恒为零的偶函数,且对任何实数x都有xf(x+1)=(1+x)f(x),则f(5/2)的值是多少?（要详细答案）

who are you help me to solve the math problem?已知函数f(x)是定义在实数集R上的不恒为零的偶函数,且对任何实数x都有xf(x+1)=(1+x)f(x),则f(5/2)的值是多少?（要详细答案）
∵xf(x+1)=(1+x)f(x)
∴f(x+1)=(1+x)f(x)/x
∴f(5/2)=f(3/2)×5÷3
f(3/2)=f(1/2)×3
f(1/2)=-f(-1/2)
∵f(x)是R上的不恒为零的偶函数
∴f(1/2)=f(-1/2)
∴f(1/2)=0
∴f(3/2)=0
∴f(5/2)=0
感觉结果有点怪,但是步骤应该没错的啊

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