As follows:
If f(2x - 1) is divisible by 2x, what is f(x) divisible by?
Polynomial
2012-04-23 6:37 am
回答 (4)
2012-04-23 10:12 am
✔ 最佳答案
I am with the first floor, but should the step be like this?f(2x - 1) = Q(x) * 2x ----(1)
Let u = 2x - 1
x = (u+1)/2
Change all the x into u in (1)
f(u) = Q[(u+1)/2] * 2[(u+1)/2]
f(u) = Q[(u+1)/2] * (u+1)
[Change the variable u back to x]
f(x) = Q[(x+1)/2] * (x+1)
So, f(x) is divisible by (x + 1)
參考: 經數學人 ronaldchik.blogspot.com
2012-04-24 5:53 am
TamT:
f(2x - 1) is divisible by 2x. Not f(2x + 1) is divisible by 2x.
f(2x - 1) is divisible by 2x. Not f(2x + 1) is divisible by 2x.
2012-04-23 9:48 am
2012-04-23 8:05 am
f(2x - 1) = Q(x) * 2x
Let y = 2x - 1
f(y) = Q(2y - 1) * (y + 1)
So, f(x) is divisible by (y + 1)
2012-04-23 14:15:55 補充：
Sorry. f(x) is divisible by (x + 1)
Let y = 2x - 1
f(y) = Q(2y - 1) * (y + 1)
So, f(x) is divisible by (y + 1)
2012-04-23 14:15:55 補充：
Sorry. f(x) is divisible by (x + 1)
收錄日期: 2021-04-13 18:39:16
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120422000051KK00927