High school math problems for detailed explanations, urgently

1.Solution: When x=-x, f(-x)+g(-x)=f(x)-g(x)=1 (-x-1).

Add and subtract g(x) from the original formula to obtain 2f(x)=1 (x-1)-1(x+1)=2 (x-1).

f（x）=1/(x²-1).

The answer is A2Proof:

1) When x=0, y=0, f(x)+f(y)=f(0)+f(0)=f(0).

That is, 2f(0)=0 f(0)=0

When y=-x, f(x)+f(-x)=f(x-x)=f(0)=0f(x) is an odd function.

2) f(x)<0 at x<0

f(x) decreases when x<0.

f(x) is an odd function.

f(x) is a subtractive function on r.

Chemistry. h²s+ohˉ=h²o+hsˉ

is an even function, f(x)=f(-x).

g(x) is an odd function, g(-x) = -g(x) simultaneous equation: f(x) + g(x) = 1x-1

f（x）-g（x）=-1x-1

Solve equations.

Write the ion equation for H2S into NaOH solution: Hs + 2OH = 2H O+S

（1）., the straight line with slope of 1 passes through the focus of the parabola y 2=4x, and intersects the parabola at two points a and b, and the length of the line segment ab is found.

Solution: p=2, focal f(1,0), linear equation y=x-1, substituting the parabolic equation.

x-1) =4x, x -6x+1=0, let a(x,y), b(x,y).

So x +x = 6; y₁+y₂=(x₁-1)+(x₂-1)=(x₁+x₂)-2=6-2=4

x₁x₂=1， y₁y₂=(x₁-1)(x₂-1)=x₁x₂-(x₁+x₂)+1=1-6+1=-4

Therefore ab = [(x -x) y -y ) =[ (x +x ) y +y ) 4(x x +y y )]

2), passing through the point M (as a straight line L with a slope of 1, the parabola y 2=4x at two points. Ask for itab|

Solution: Linear equation: y=x-2, substituting the parabolic equation yields:

x-2)²=4x，x²-8x+4=0.Let a((x,y),b(x,y).

So x +x =8, y +y = (x -2) + (x -2) = (x +x )-4 = 8-4 = 4

x₁x₂=4， y₁y₂=(x₁-2)(x₂-2)=x₁x₂-2(x₁+x₂)+4=4-16+4=-8

Therefore ab = [ (x +x ) y +y ) 4(x x +y y )]= [64+16-4(4-8)]= 96=4 6

(1) The focus is (1,0), so the straight line is y=x-1 to solve the equation x1=3-2*2, y1=2-2*2;

or x2=3+2*2, y2=2+2*2.

then d = ((y2-y1) + x2-x1) ) ) = 8

Use the chord length formula: |ab|=√(1+k^2)*|x1-x2|= (1+k 2)* x1+x2) 2-4*x1*x2], where k is the slope of the straight line, x1, x2 are the two roots of the linear equation and the quadratic curve after eliminating y about x, according to the chord length formula, x1, x2 does not need to be solved, only the relationship between the root and the coefficient can be calculated.

Substituting it, a2=3 -1=-3 a3=1 2 a4=3 a5=-2 a6=-1 3 a7=1 2 That is to say, starting from a3 to a6 is a cycle, and the product of this cycle is 1, 2008 4 is exactly an indigo, so a bunch of 1 multiplication is still 1, which is actually a1*a2=-6

f(x)=cos(2x+3)ten(1-cos2x)2

(root number 3 2) sin2 x ten 1 2

The maximum value one (root number 3) 2 ten-1 2