A few questions about parity analysis are urgent, and the good chase score is 20

Khan 3 Miscellaneous 2003 2=1001......1 A school goes to 1002 students in the morning, then the second school goes to 1001, the first school goes to 1001 students in the afternoon, and there is 1 more place than in the afternoon, and there is one more seat, and the second school is going to 1002, and there happens to be a seat that is sat twice by classmates from 2 schools, and the other situation is very clear: 4, that is 1+9+7+9, to be divided by 3.

Even Functions: First, the localized sense is symmetrical with respect to the origin x [-5,-2], x [2,5].

Second, f(-x) = f(x). So it's an even function.

f(x)=lg[(sinx)+root(1+sin 2x)]f(-x)=lg[(sin-x)+root(1+sin 2x)]=lg[-sinx+root(1+sin 2x)]=lg[1 root(1+sinin 2x)+sinx]=lg[root(1+sin 2x)+sinx] (1)=-lg[root(1+sin 2x)+sinx]=-f(x)odd function.

When a=0, f(x)=x|x|，f(-x)=-x|x|=-f(x), where f(x) is an odd function;

When a≠0, f(a)=0 and f(-a)=-2a|a|≠0, f(x) is not odd or even.

That's the right solution.

If it is divided into two categories, greater than or equal to a and less than a, then the answer when it is greater than a is to be rounded, and it is not true when it is less than a, and all should be classified by dividing it into a=0 and a≠0. Hope to adopt.

Odd and even are not the same.

This function is neither odd nor even.

The odd function should satisfy f(x)+f(-x)=0, and this function f(x)+f(-x)=-8x 2, which is not equal to 0;

The even function should satisfy f(x)-f(-x)=0, and this function f(x)-f(-x)=2x 3 is not equal to 0.

f(x)=x -4x, which defines the domain x r, and with respect to origin symmetry, f(-x)=(-x) -4(-x) =-x -4x, we know that f(-x)≠f(x), and f(-x)≠-f(-x), so it is a non-odd and non-even function.

Solution: Since f(x)=x 3-4x 2, so f(-x)=(-x) 3-4x(-x) 2=-x 3-4x 2, so f(-x)≠f(x) and f(-x)≠-f(x), so f(x) is neither an even nor an odd function.

It is neither an odd nor an even function.

f(x)=x³-4x²

f(-x)=(-x)³-4(-x)²

x³-4x²

f(-x)≠ f(x), f(-x)≠-f(x), so f(x) is a non-odd and non-even function.

That's it.

1. Introduction. Integers can be divided into two categories: odd and even. Using the classification of odd and even numbers and their special properties, some problems related to integers can be solved simply, and we call this method of solving problems by analyzing the parity of integers as parity analysis.

2. New awards. Example 1 There are 1993 dots around the circumference, and each dot is colored twice, either red and blue, all red, or all blue. Finally, the statistics show that 1993 times of dyeing red and 1993 times of dyeing blue, it is verified that at least a little of it is dyed with red and blue.

Proof: Suppose that no point is dyed red and blue, i.e., the first time it is dyed red (or blue), and the second time it is dyed red (or blue).It is advisable to assume that the first time there are m dots dyed red, and the second time there are still and only these m dots dyed red, that is, there are 2m red dots, but 2m ≠1993, at least a little bit is dyed red and blue.

Example 2 In the sequence at the beginning of 1985, each number from the fifth term onwards is equal to the single digit of the sum of the preceding digits, and it is verified that there will be no ...... in this series,1,9,8,6,……

Proof that the parity of the sequence of numbers starting with 1985 is: odd, odd, even, odd, ,......odd,The parity of the following series is "odd, odd, odd, odd, even", and 1986 is "odd, odd, even, even", so ......1,9,8,6,……Does not appear in the number sequence.

Example 3 There are 1,993 coins on the table, 1,993 coins for the first time, 1,992 coins for the second time, and 1,991 coins for the third time,......Turn one of them for the 1993rd time. Would that make all the 1,993 coins on the table face up?

Analysis: The fact that a coin can be turned face up by flipping it odd times plays a key role in solving this problem.

That is, an average of 997 flips per coin, which is an odd number. Thus, for each coin, the original downward-facing side can be turned upwards. Here's how to flip it:

1st Flip No. 1 1993; 2nd Flip 2 1993, 1993 Flip 1; 3rd Flip No. 3 1993, No. 1992; ......This happens to be the case that each coin has been flipped 997 times, with the result that the original side is turned face up.

(1) is an even function:

f(x)=︱x︱

f(-x)=︱-x︱=︱x︱

f(-x)=f(x)

2) Non-odd and non-even:

f(x)=3x^2-2x

f(-x)=3(-x) 2+2x=3(x) 2+2xf(x) ≠f(-x) and f(-x) ≠f(x)(3)y=x (1 2).

Since the domain x 0 is defined, it is inherently asymmetrical, and is generally referred to as a parity-free function, which has no parity to say.

From 3, we know that x is a positive number and the absolute value of x is equal to x y=x=root number x Only 1 satisfies x(x=root number x) x=1=y odd number.

It's all done directly according to the definition.

1. The definition domain is x r, symmetrical relative to the origin, f(-x)=|-x|=|x|=f（x）

So y=|x|is an even function.

2. The definition domain is x r, which is symmetric relative to the origin, f(-x)=3(-x) -2(-x)=3x +2x

f(-x)≠f(x), f(-x)≠-f(x), so y=3x -2x is a non-odd and non-even function.

3. The definition domain is x 0, which is not symmetrical with respect to the origin, so it is a non-odd and non-even function.