已知偶函数y=f(x)满足条件f(x+1)=f(x-1),且当x∈[-1,0]时,f(x)=3x+4/9,则f(log1/35)的值等于_.

问题描述:

已知偶函数y=f(x)满足条件f(x+1)=f(x-1),且当x∈[-1,0]时,f(x)=3x+

4
9
,则f(log
1
3
5)
的值等于______.

由f(x+1)=f(x-1),得f(x+2)=f(x),
所以f(x)是以2为周期的周期函数,
又f(x)为偶函数,
f(log

1
3
5)=f(-log35)=f(log35)=f(log35−2)=f(log3
5
9
)
=3log3
5
9
+
4
9
=
5
9
+
4
9
=1

故答案为:1.