Given that the function y = f (x) satisfies f (2x-3) = 4x2-x + 1, X ∈ [0,2], find the analytic expression and definition of F (x)

Given that the function y = f (x) satisfies f (2x-3) = 4x2-x + 1, X ∈ [0,2], find the analytic expression and definition of F (x)

Because x belongs to [0,2] 2x belongs to [0,4] 2x-3 belongs to [- 3,1], that is, its domain is [- 3,1], let t = 2x-3, then x = (T + 3) / 2F (T) = 4 * [(T + 3) / 2] ^ 2 - [(T + 3) / 2] + 1 = (T + 3) ^ 2-T / 2-1 / 2 = T ^ 2 + 6T + 9-t / 2-1 / 2 = T ^ 2 + 11T / 2 + 17 / 2, so f (x) = x ^ 2 + 11x / 2 + 17 / 2

The equation (3x + 2) = 4 (x-3) is transformed into the general form of quadratic equation with one variable, and its quadratic coefficient, linear coefficient and constant term are written out

(3x+2)=4(x-3)
3x+2=4x-12
x-14=0
0x²+x-14=0
The coefficient of quadratic term is 0, the coefficient of primary term is 1, and the constant term is - 14

The second power of solving equation (2x-3) is equal to (2x + 1) (2x-1) - 2

4x²-12x+9=4x²-1-2
-12x=-12
∴x=1

Let n-dimensional vector group A1, A2, A3 be linearly independent. Prove that vector group A1 + 2A2, A2 + 2A3, A3 + 2a4 are linearly independent. Find the detailed process of solving the problem

Let there be a group of numbers, K1, K2, K3, such that K1 (a1 + 2A2) + K2 (A2 + 2A3) + K3 (A3 + 2A1) = 0. We can get: (K1 + 2K3) a1 + (2K1 + K2) A2 + (2k2 + K3) A3 = 0. Because A1, A2, A3 are linearly independent, K1 + 2K3 = 02k1 + K2 = 02k2 + K3 = 0. The solution is: K1 = K2 = K3 = 0, so vector group A1 + 2A2, A2 + 2A3, A3 + 2A

M minus 4) times the square of X - (m-2) times x plus 8 = 0 is the one variable linear equation of X
(1) Find the algebraic formula:
2003（m-x)（x-4m）-3m+2x-6
(2) Find the equation about y
The solution of the absolute value of (M-3) (x-4m) * 2Y = X-2

（1）-4；
（2）1/15

If the even function f (x) (x ∈ R) satisfies f (x + 2) = f (x) and X ∈ [0,1], f (x) = x, then the number of roots of the equation f (x) = log3 | x | is ()
A. 2 b. 4 C. 3 d. more than 4

When x ∈ [0,1], f (x) = x, so when x ∈ [- 1,0], f (x) = - X. then the number of roots of the equation f (x) = log3 | x | is equal to the number of intersections between the image of function y = f (x) and the image of function y = log3 | x | in the same coordinate system As shown in the figure: obviously, there are four intersections between the image of function y = f (x) and the image of function y = log3 | x | so B

A polynomial x ^ 2 + 1, add a complete square formula to make it a polynomial, write out all the possibilities, and write out the appearance of merging after adding

2x (x+1)²
-2x (x-1)²
¼x^4 (½x²+1)²

The maximum value of the function FX = root sign three SiNx + cos (one third π + x) is

3sinx+cos（π/3+x)
=3sinx+1/2cosx-v3/2sinx
=(3-v3/2)sinx+1/2cosx
According to the formula asinx + bcosx = V (a ^ 2 + B ^ 2) sin (x + θ)
V [(3-v3 / 2) ^ 2 + 1 / 4] is the maximum

The inverse of 1 to the third power minus (1 + 0.5) times 1 / 3 divided by (negative 4)

The third power of 1 is 1 (i.e. 1 × 1 × 1). The opposite number of 1 is - 1 (negative one). The listing formula: - 1 - (1.5 × 1 / 3) / (- 4) = - 1 - (3 / 2 × 1 / 3) × (- 1 / 4) = - 1-1 / 2 × (- 1 / 4) = - 1 - (- 1 / 8) = - 1 + 1 / 8 = - 7 / 8

If the words "220 V & nbsp; 5A" are marked on an electric energy meter, the total power of all electrical appliances shall not exceed______ W. The lamp can be equipped with "pz220-60" at most______ A cup of tea

When using the meter, the total power of all electrical appliances: P = UI = 220V × 5A = 1100W; the maximum number of lamps that can connect "220V & nbsp; & nbsp; 60W" is: 1100w60w ≈ 18.3. So the answer is: 1100; 18