问题
解答题
已知f(x)=
|
答案
f(x)= 1 2x+ 2 ∴f(0)+f(1)=
+1 20+ 2
=1 21+ 2
;,f(-1)+f(2)=2 2
+1 2-1+ 2
=1 22+ 2 2 2 f(-2)+f(3)=
+1 2-2+ 2
=1 23+ 2 2 2
归纳猜想一般性结论:f(-x)+f(1+x)=
.(6分)2 2
证明如下:f(-x)+f(x+1)
=
+1 2-x+ 2
=1 2x+1+ 2
+2x 1+
•2x2 1 2x+1+ 2
=
+
•2x2
+2x+12
=1 2x+1+ 2
=
•2x+12
+2x+12
•2x+12
(1+2
•2x) 2
=
(10分)2 2