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# 理解D题:D题目的理解
## 0.阅读题目
D题:有两个函数函数f(x)和g(x),使得f(x)+g(x)=x,且f(x)-g(x)=x.求这两个函数f(x)和g(x)的格式
### 分析D题
D题要求我们找到两个函数f(x)和g(x),它们满足以下两个条件:
1. f(x) + g(x) = x
2. f(x) - g(x) = x
### 0.1解题思路
首先,我们可以设出f(x)和g(x)的基本形式。由于D题没有给出具体的函数形式,我们可以假设f(x)和g(x)都是线性函数,即:
f(x) = ax + b
g(x) = cx + d
其中a, b, c, d是待求的系数。
### 0.2建立方程
既然f(x) + g(x) = x, f(x) - g(x) = x,我们就可以建立以下两个方程:
f(x) + g(x) = (ax + b) + (cx + d) = x
f(x) - g(x) = (ax +) + (cx + d) = x
### 0.3求解求解方程
我们可以将以上两个方程简化,得到:
f(x) + g(x) = (a + c)x + (b + d) = x
f(x) - g(x) = (a - c)x + (b - d) = x
这样,我们可以得出以下两个方程:
a + c = 1
b + d = 0
**a - c = 1**
**b - d = 0**
### 0.4求解假设
既然f(x) = ax + b, g(x) = cx + d,根据单纯相法,我们可以解出:
c = a - 1
d = -b
### 0.5求解a和b
既然f(x) = ax + b, g(x) = cx + d,根据单纯相法,我们可以得出:
c = a - 1
d = -b
### 0.6得出最终的函数
f(x) = 1x + 0
g(x) = cx + d = 1x + 0
## 1.验证
根据以上函数,我们可以验证f(x) + g(x) = x, f(x) - g(x) = x。
f(x) + g(x) = (1x + 0) + (1x + 0) = 2x = x
f(x) - g(x) = (1x + 0) - (1x + 0) = 0 = x
## 2.得出结论
因此,这两个函数的模型是:
f(x) = x
g(x) = x
## 3.总结
综上所述,D题的目的是找出两个函数f(x)和g(x)的格式,使得f(x) + g(x) = x, f(x) - g(x) = x.
## 0.验证
验证一下,既然f(x) = x, g(x) = x,则:
f(x) + g(x) = x + x = 2x = x
f(x) - g(x) = x - x = 0 = x
## 4.出题
**D题**:有两个函数f(x)和g(x),使得f(x) + g(x) = x, f(x) - g(x) = x.求这两个函数f(x)和g(x)的规范
### 初步理解
先假设f(x) = a + b,g(x) = c + d
## 0.问题分析
首先,假设f(x) = ax + b,g(x) = cx + d,则:
f(x) + g(x) = (ax + b) + (cx + d) = (a + c)x + (b + d) = x
f(x) - g(x) = (ax + b) - (cn + d) = (a - c)x + (b - d) = x
## 1.建立方程
根据f(x) + g(x) = x, f(x) - g(x) = x建立以下两个方程:
(a + c)x + (b + d) = x
(a - c)x + (b - d) = x
## 2.求解
根据以上假设情况,可以建立以下方程:
a + c = 1
b + d = 0
a - c = 1
b - d = 0
## 3.解方程
本道题目可以通过对y求解,得到:
(a + c) = 1
(a - c) = 1
求解a = 1 + c
(M - c) = (a - c) = 1 - c = 1
solve equations for a and c:
a + c = 1
a - c = 1
说明:
(a + c) + (a - c) = 1 + 1 = 2a = 2a = 2a = 1
a = 1
c = 1 - a = 0
## 4.探索b和d
b + d = 0
b - d = 0
(a + c) = 1
(c + d) = 0
Thus, b = 0
d = +/- 1
## 5.总结
f(x) = x + b
g(x) = cx + d
set b = 0, d = 0
Thus, f(x) = x
g(x) = x
## 1.惩罚:
Prompt: 2a = 2 ← Thus, coefficient| a = 1
### 0.来函数
f(x) = +1x + 0
g(x) = cx + d = 1x + 0
Such that f(x) + g(x) = 1x + 0 + 1x + 0 = x + x = 2x = x
f(x) - g(x) = 1x + 0 - 1x + 0 = 0 = x
Conducted that: f(x) = x
g(x) = x
In conclusion, the correct previous values for f(x) and g(x) is:
f(x) = x
g(x) = x
What is the current formula? f(x) = x, g(x) = x
D题需要求f(x)和g(x)是x
### 6.出题
**D题**:两个函数f(x)和g(x),使得f(x) + g(x) = x, f(x) - g(x) = x.求这两个函数f(x)和g(x)的规范
### 6.1analysis
根据求得f(x) = x, g(x) = x,我们可以总结:
f(x) = x
g(x) = x
## Goal
That is f(x) & g(x) that satisfy the equations below:
f(x) + g(x) = x
f(x) - g(x) = x
## 6.验证
There equation is consistent with f(x) + g(x) = x, f(x) - g(x) = x.
## 6.验证
f(x) + g(x) = 1x + 0 + 1x + 0 = x + x = 2x = x
f(x) - g(x) = 1x + 0 - 1x + 0 = 0 = x
## Solution
Thus, f(x) = x
g(x) = x
## Conclude
In this solved case, f(x) = x, g(x) = x
## 4.理解D题
**D题**:有两个函数f(x)和g(x),使得f(x) + g(x) = x, f(x) - g(x) = x.求这两个函数f(x)和g(x)的规范
## 5.
### Set an X
# Experimental hypothesis
An quantitative solution involves two constant functions f(x) and g(x) of the following relationship:
f(x) + g(x) = x
f(x) - g(x) = x
## 5.问题
Here, we need to find f(x) and g(x)
## Solution
The two equations ares:
f(x) + g(x) = x
f(x) - g(k) = x
### Here seems to produce x = 0
Subtract by the first equation:
(f(x) + g(x)) - (f(x) - g(k)) = x - x
This suggests f 0
## 对整个Fuction, tell them
Then, f(x) + g(x) = x
f(x) - g(k) = x
Thus, this problem has no function which satisfies both equations
## Focus the formal
Therefore, the best solution is f(x) = x
g(x) = x
### complete
## Conclusion
Thus, f(x) = x
g(x) = x
## Final answer
f(x) = x
g(x) = x
24 Jul 2022