If the domain of function f (x + 1) is [0,2], find the domain of function y = f (x2)

If the domain of function f (x + 1) is [0,2], find the domain of function y = f (x2)

The domain of solution of F (x + 1) is [0,2]
Then x belongs to [0,2]
Then 0 ≤ x ≤ 2
Then 1 ≤ x + 1 ≤ 3
So the range of the corresponding rule f is [1,3]
So for the function y = f (x2)
1≤x^2≤3
The solution is 1 ≤ x ≤√ 3 or - √ 3 ≤ x ≤ - 1
So the definition field of function is {X / 1 ≤ x ≤ √ 3 or - √ 3 ≤ x ≤ - 1}

2.4+0.5x=3.8
3.6x-x=3.12
4（a-22.5）=5.8

2.4+0.5x=3.8
0.5x=3.8-2.4
0.5x=1.4
x=2.8
3.6x-x=3.12
2.6x=3.12
x=1.2
4（a-22.5）=5.8
4a-90=5.8
4a=5.8+90
4a=95.8
a=23.95

The original price of a TV set was 1200 yuan. First, the price was increased by 1 / 5, then decreased by 1 / 4. Now, how much is the price of the TV set?
It is helpful for the responder to give an accurate answer

1200*(1+1/5)*(1-1/4)=1080

(2005+2004*2006)/(2005*2006-1)
Calculation questions: (2005 + 2004 * 2006) / (2005 * 2006-1)

[2005+(2005-1)*(2005+1)]/[2005*(2005+1)-1]=(2005*2005+2005-1)/(2005*2005+2005-1)=1
So the final result is 1

1. It took 10 hours for a ship to go from place a in the upper reaches of the river to place B in the lower reaches of the river at a constant speed. It took 12 hours for a ship to return from place B to place a at a constant speed. The water velocity in this section of the River is 3 km / h, and the still water velocity X of the ship to and fro does not change. What conditions does x meet?
2. Lao Zhang and Lao Li bought the same number of rabbits. One year later, the number of rabbits raised by Lao Zhang increased by two compared with the number of rabbits bought. Lao Li raised one less than twice the number of rabbits bought. The number of rabbits raised by Lao Zhang did not exceed 2 / 3 of Lao Li's. how many rabbits did Lao Zhang buy a year ago?

1.
10(x+3)=12(x-3)
10x+30=12x-36
2x=66
x=33
two
Suppose Lao Zhang bought x rabbits a year ago, so did Lao Li
x+2≤2/3*(2x-1)
3x+6≤4x-2
x≥8
So a year ago, Lao Zhang bought at least eight rabbits

If a commodity is sold at a fixed price, the profit will be 960 yuan. If it is sold at 80% of the fixed price, the loss will be 832 yuan. What is the purchase price of this commodity

Suppose the purchase price is X
（x+960）80%=x-832,
Using the above formula, we can solve X and get x = (960 × 80% + 832) / (1-80%) = 8000
The purchase price is 8000 yuan

The speed of the earth around the sun is about 1.1 × 10 5 km / h, and the speed of sound in the air is about 340 m / s

340m/s=1224km/h

Mathematical problems with two unknowns

1. There are 45 heads and 146 feet in the same cage. How many are there in each cage?
2. A factory bought 56 tons of a and B materials, which cost 9860 yuan. If 190 yuan per ton of a material and 160 yuan per ton of B material, how many tons of each material?
3. If every four students sit on a bench, 28 students have no seat. If six students sit on a bench, the number of students and the number of benches are calculated
4. A factory bought 56 tons of a and B materials, which cost 9860 yuan. If 190 yuan per ton of a material and 160 yuan per ton of B material, how many tons of each material?
5. In a certain unit, a and B got 9000 yuan in cash last year and 12700 yuan in cash this year. It is known that the amount of cash they got this year increased by 50% for a and 30% for B. how many yuan for each of them this year?

The coordinate of point (A.B) about X-axis symmetry is y, the coordinate is origin, and the coordinate of symmetric point is y

X-axis symmetry means that the ordinate is opposite
Y-axis symmetry is the opposite abscissa
Origin symmetry means that the vertical and horizontal coordinates are opposite
The coordinates of the point (A.B) which is symmetric about X axis are (a, - b)
The coordinates of y-axis symmetry are (- A, b)
The coordinates of the point symmetrical about the origin are (- A, - b)
It is suggested to use points (2,3) to mark each point in rectangular coordinate system
In this way, we can understand these abstract concepts more quickly

38 × 1 1 / 1999 + 8 × 1 / 1999 + 1998 × 1 / 18 / 36 (simple algorithm)

38*(2000/1999)+[(8*1999+1998)/1999]*(19/18)*36
=38*(2000/1999)+[(9*2000-10)/1999]*38
=38*(10*2000-10)/1999
=38*10
=380