令f(x)滿足:f(1)=1/2;f(2)=1/4;f(3)=1/4;得f(x)。從而得f(4)。

來源: 2010-09-08 08:16:14 [博客] [舊帖] [給我悄悄話] 本文已被閱讀:

方法之一:令f(x)是一個二次函數。
f(x) = a*x^2 + b*x + c

用係數待定法求a,b,c

f(1) = a + b + c = 1/2 ----------------------(1)

f(2) = 4a + 2b + c = 1/4 ---------------------(2)

f(3) = 9a + 3b + c = 1/4 ---------------------(3)

(3)-(2)
5a + b = 0 ---------------------------(4)

(2)-(1)
3a + b = -1/4 ------------------------(5)

(4)-(5)
2a = 1/4
a = 1/8

將a值代入(5)得
b = -5/8

將a,b值代入(1)得
c = 1/2 - 1/8 + 5/8 = 1

將a,b,c 值代入f(x)得
f(x)= 1/8*x^2 - 5/8*x + 1

令x = 4

f(4)= 1/8*16 - 5/8*4 + 1 = 2 - 5/2 + 1 = 1/2