请教一道数学题, waiting on line

andiewang1

f(x)=f(1-x) for all x ?

a: f(x)=1-x

b: f(x)=1-x^2

c: f(x)=x^2-(1-x)^2

d: f(x)=x^2 (1-x^2)

e: f(x)=x/1-x

answer : d

请问这种应该怎样做, 我把
    y=1-x, 代到5个式子, 得不出来.

我数学实在是差呀,   能帮助我讲一讲思路和过程吗?

先谢谢了

[此贴子已经被作者于2008-3-7 12:57:44编辑过]

macelino

f(x)=f(1-x)

看A：f(x)=1-x，f(1-x)=1-(1-x)=x，那么显然，f(x)与f(1-x)不等

其他都按这个方法算一下就知道。f(x)和f(1-x)分别求，看右边等不等

andiewang1

谢谢, macelino

我是按照你的方法做的, 但是得不出来, 你能帮我把5个式子的过程推导过程写出来吗?

另有一题, 还想问一问怎么算的

On Jane's credit card account, the average daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days. At the begining of a certain 30-day billing cycle, Jane's credit account had a balance of $600. Jane made a payment of  $300  on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle?
(1) Jane's payment was credited on the 21st day of the billing cycle
(2) The average daily balance through the 25th day of the billing cycle was $540
答案是D

andiewang1

ding

mizue123

数学解题过程：
对于(1):前20天每天的余额是600,因为第21天用去300,所以从第21天到第30天的账户余额都是300; 所以average daily balance为"(600*20+300*10)/30"

对于(2):由于前25的平均值为540,说明在前25天的某一天，用去了300(若没有用，则平均值应该为600),所以设在第x天用去300,得出等式：25*540=(x-1)*600+[25-(x-1)]*300; 解出x的值；此后过程同上(1)

andiewang1

thanks, but i am still confusing the first one.