Let f (x) be a function defined from negative infinity to positive infinity, then it is proved that the function can represent an even function and a function Sum of odd functions

Let f (x) be a function defined from negative infinity to positive infinity, then it is proved that the function can represent an even function and a function Sum of odd functions

Let g (x) = [f (x) + F (- x)] / 2. H (x) = [f (x) - f (- x)] / 2. Obviously, G (x) = g (- x), H (x) + H (- x) = 0. F (x) = g (x) + H (x)

1. Factorization of - 3A ^ 3B + 12ab ^ 3 2, 2A ^ 2b-4ab ^ 2

Let the definition field of function y = f (x) be R +, and f (XY) = f (x) + F (y), f (8) = 3, then what is f (2)?

f(8)
=f(4×2)
=f(4)+ f(2)
f(4)
= f(2×2)
= f(2) + f(2)
So f (8) = f (2) + F (2) + F (2) = 3
3f(2) = 3
f(2) =1

Because X & # 178; - x + 2 = (x-1 / 2) &# 178; + 7 / 4 > 0, X (X & # 178; - x + 2)

The constant of X & # 178; - x + 2 = (x-1 / 2) &# 178; + 7 / 4 > 0 holds
But x (X & # 178; - x + 2)

A color TV set costs 508 yuan. First, it will be reduced by 1 / 10 and then increased by 1 / 10. What's the current price?

508 * (1-tenth) = 457.2
First calculate the price after the price reduction, and then take the price after the price reduction to increase the price,
457.2 * (1 + tenth) = 502.92
The current price is 502.92 yuan
Welcome to continue to ask

The calculation of fractional square
Square of (12 / 16-3 / 6)
How to calculate?

（12/16-3/6）^2
=(36/48-24/48)^2
=(1/4)^2
=1/16

The purchase price of a certain commodity is 1250 yuan, which is marked at 120% of the purchase price. The shop allows the salesperson to discount at a profit of no less than 8%. How much is the lowest discount for the salesperson?

Price: 1250 * 120% = 1500 yuan,
Profit not less than 8%: 1250 * 8% = 100 yuan,
(1250 + 100) / 1500 = 0.9 = 90%
Salesmen can sell this product at a minimum of 10% discount. The equation is: set a minimum of X% discount
1250*120%x=1250*8%
Solution 1500x = 1350
X=0.9
A: the minimum discount is 10%

A commodity cost 80 yuan per piece, selling price 100 yuan, sold 100 pieces per day
If the selling price is reduced by X%, the number of goods sold will increase by 16%. If the daily turnover of the goods is required to be at least 10260 yuan, and no loss can be made, the value range of X is calculated

The first condition
(selling price 100 * x) * (sales quantity 100 * 1.6x) > 10260
16000*X*X>10260
10> In the case of 0.800780868902348, the turnover is at least 10260
Second, we should not lose money
If 100 * x > 80, there will be no loss
So x > 0.8
Finally, according to two conditions, if x > 0.800780868902348, it can be rounded
10> 81 two decimal places

It is known that the (1993 + a) power of 1993 + the (1994 + b) power of 1994 can be divided by 5, where a is greater than or equal to 0 and less than or equal to 2; B is greater than or equal to 1 and less than 2
It is known that the (1993 + a) power of 1993 + the (1994 + b) power of 1994 can be divided by 5, where a is greater than or equal to 0, less than or equal to 2; B is greater than or equal to 1, less than or equal to 3; find a and B

The mantissa of a = 1, B = 2.xxx3 is as follows: Power: 0, 1, 2, 3, 4, 5 Mantissa: 1, 3, 9, 7, 1, 3 Counting from 0 to 4 is a cycle. Similarly, the mantissa of the power of xxx4 is like the following cycle: power 1, 2, 3, 4, 5 Mantissa: 4, 6, 4, 6, 4 Count one from one to two

In the shape of a ring, its area is 200cm, the radius of the outer circle is 10cm, and the radius of the inner circle is 10cm?
To calculate the process result, don't write the result directly,

Let the radius of the small circle be xcm,
10^2*3.14-(X^2)*3.14=200
314-3.14X^2=200
-3.14X^2=-114
X = about 6.03