Given that the domain of even function f (x) is r, if x ≥ 0, f (x) = - x ^ 2 + 2x + 2, find the expression of F (x) on R

Given that the domain of even function f (x) is r, if x ≥ 0, f (x) = - x ^ 2 + 2x + 2, find the expression of F (x) on R

x0
So f (- x) is suitable for f (x) = - X & sup2; + 2x + 2
f(-x)=-x²-2x+2
Even function then f (x) = f (- x)
therefore
f(x)=
-x²-2x+2,x＜0
-x²+2x+2,x≥0
Add a brace

Given that the domain of function f (x) is [- 1 / 2,1 / 2], find the domain of function y = f (X & # 178; - X-1 / 2)

-1/2≤x²-x-1/2≤1/2
0≤x²-x≤1
1/4≤x²-x+1/4≤5/4
1/4≤(x-1/2)²≤5/4
1 / 2 ≤ X-1 / 2 ≤ √ 5 / 2, or - √ 5 / 2 ≤ X-1 / 2 ≤ - 1 / 2
Then 1 ≤ x ≤ (1 + √ 5) / 2, or (1 - √ 5) / 2 ≤ x ≤ 0
The domain of definition is [(1 - √ 5) / 2,0] ∪ [1, (1 + √ 5) / 2]

Given that the domain of F (x) is [- 1,1], find the domain of (1) y = f (x + 1) (2) y = f (X & # 178;)

We know that the domain of F (x) is [- 1,1] (1) y = f (x + 1) (2) y = f (X & # 178;)
(1) Then - 1 ≤ x + 1 ≤ 1
The solution is: - 2 ≤ x ≤ 0
The domain of definition of y = f (x + 1) is [- 2,0]
(2) Then - 1 ≤ x ^ 2 ≤ 1
The solution is: - 1 ≤ x ≤ 1
The domain of definition of y = f (X & # 178;) is [- 1,1]

Given that the domain of the function y = f (X & # 178; + 1) is [- 2,3], find the domain of the function x = f (x)

The definition field of y = f (x ^ 2 + 1) is [- 2,3)
Let z = x ^ 2 + 1
Then the range of Z is [1,9]
That is, the domain of y = f (z) is [1,9]
That is, the domain of y = f (x) is [1,9]

A truck drives from a to B, and three hours after departure, a car also drives from a to B. the car arrives at B 20 minutes later than the truck. It is known that the speed of the truck is 20 kilometers per hour, and the speed of the car is two times faster than that of the truck

Suppose the distance between a and B is x km, 20 minutes = 13 hours, 20 × 2 = 40 (km), & nbsp; x20-x40 = 3-13, & nbsp; & nbsp; & nbsp; 140x = 223140x △ 140 = 223 △ 140, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 10623, a: the distance between a and B is 10623 km

When drawing the number axis, must the unit lengths of the left and right sides of the origin be the same? Must a unit length represent a unit

The unit length of the left and right sides of the origin must be the same! A unit length must represent a unit or its multiple

From city a to city B, the bus takes 8 hours, and the truck takes 12 hours. The two cars come out from the two places at the same time. After meeting, they arrive at the two cities and return immediately. After a few hours, they meet again

Set the distance to 1
The speed of passenger car is 1 / 8, the speed of freight car is 1 / 12, and the encounter time is 1 ÷ (1 / 8 + 1 / 12) = 4.5 hours
The truck returns in 12 hours. At this time, the bus has been on the return road for 4 hours, which is 1 / 2 of the distance
The second meeting time = 1 / 2 △ 1 / 8 + 1 / 12 = 2.25 hours
I don't understand. I'll give you a comment. Thank you

Definition: A is a rational number which is not 1. We call 1 / 2 of 1-A as the difference reciprocal of A. for example, the difference reciprocal of 2 is 1-2 / 1 = - 1, the difference reciprocal of - 1 is 1 - (- 1) 1 = 2 / 1, A1 = - 3 / 1, A2 is the difference reciprocal of A1, A3 is the difference reciprocal of A2=----------------------------

Three quarters

Parachutists perform low altitude parachuting. When the car flies 224m above the ground, the athletes leave the plane to do free fall in the vertical direction

Let: the displacement of the free falling body is H1, the displacement of the second half is H2, then: H1 = 1 / 2gt1 ^ 2h2 = gt1t2-1 / 2at2 ^ 2h1 + H2 = 224gt1-at2 = 5, so the solution is T1 = 5S, T2 = 3.6s, H1 = 125m, h2 = 99mh3 = 1 / 2gt2 ^ 2 = 1 / 2 * 10 * 3.6 ^ 2 = 64.8mt = T1 + T2 = 8.6s, so answer: the minimum height from the ground is 99m

72% of 4 / 9 is equal to a number minus 3 / 7. What's the number?

Let x-3 / 7 = 4 / 9 × 72%, x-3 / 7 = 8 / 25, x = 131 / 175