问题 填空题
函数f(x)=
x
x2+1
,则
f(2)
f(
1
2
)
+
f(3)
f(
1
3
)
+
f(4)
f(
1
4
)
+…+
f(2009)
f(
1
2009
)
=______.
答案

f(x)=

x
x2+1

f(

1
x
)=
1
x
(
1
x
)
2
+1
=
x
x2+1

f(x)
f(
1
x
)
=1

f(2)
f(
1
2
)
+
f(3)
f(
1
3
)
+
f(4)
f(
1
4
)
+…+
f(2009)
f(
1
2009
)
=2008

故答案为:2008

阅读理解与欣赏
问答题