Question

设f(x)是定义在R上的偶函数，且f(1+x)= f(1－x),当－1≤x≤0时， f (x) = － x，则f (8.6 ) = _________

Answer 1

解：∵f(x)是定义在R上的偶函数∴x = 0是y = f(x)对称轴；
又∵f(1+x)= f(1－x) ∴x = 1也是y = f (x) 对称轴。故y = f(x)是以2为周期的周期函数，∴f (8.6 ) = f (8+0.6 ) = f (0.6 ) = f (－0.6 ) = 0.3

Answer 2

题目错了，他解答的是f(x)=-1/2x是的该题
答案就是 0.3

Answer 3

f(0.6) = f(-0.6) = 0.6
f(x)= f(1+x-1)=f(1-x+1)=f(2-x)= f(x-2) = f(x-2+2)
所以 f(x)=f(x+2)
周期为2
f(x)=f(x+8)

f(8.6)=f(8+0.6)=f(0.6)