It is known that the function f (x) defined on R satisfies: for any real number a, B, there is always f (a + b) = f (a) + F (b) (1) Find f (0); (2) judge the parity of F (x). (3) if x > 0, f (x) > 0. Judge the monotonicity of F (x). And give the proof

(1) let a = b = 0, then f (0) = f (0 + 0) = f (0) + F (0) ‖ f (0) = 0. (2) let a = - B, then 0 = f (0) = f (a + (- A)) = f (a) + F (- a) ‖ f (- a) = - f (a), that is, the function is odd. (3) let X1 < X2, then x2-x1 > 0, ‖ f (x2-x1) > 0f (x2) - f (x1) = f (x1 + (x2-x1)) - f (x1) = f (x1) + F (x2-x1) - f (x1) = f (x2-x1)

The maximum and minimum of the decreasing function f (x) with the domain [a, b] are

The maximum value is f (a) and the minimum value is f (b)

1、 The square of 1000 = the third power of 100 2.246810 guess two idioms?

1、 Equal measure
2、 It's a coincidence

If the monomial x a squared plus a Y cubic is the same as the two X Cubic y B, then the B power of a

X ^ (a ^ 2 + 1) y ^ 3 and 2x ^ 3Y ^ B are of the same type,
Then: A ^ 2 + 1 = 3,3 = B,
——》a=+-v2,b=3,
——》a^b=(+-v2)^3=+-2v2.

If the intersection of the line y = 3x + m and the line y = 4-2x is on the X axis, then M=______ ．

When y = 0, 4-2x = 0, the solution is x = 2, so the intersection coordinate of the line y = 4-2x and the X axis is (2, 0), and then (2, 0) is substituted into y = 3x + m, 0 = 3 × 2 + m, the solution is m = - 6

If the intersection of the line y = 2x + m and the line y = 3x-4 is on the X axis, then the value of M is

y=2x+m
y=3x-4
y=0
∴x=4/3
y=0
m=-8/3
The intersection point is on the X axis, y = 0, substituting y = 0 into y = 3x-4 to get x = 4 / 3, substituting x = 4 / 3 into y = 2x + m to get m = - 8 / 3

If the intersection of the line y = x + m and the line y = - 2x + 4 is on the X axis, then M is equal to?

Y = 0 on X-axis
That is, when y = 0, two Y are equal
y=x+m=0
x=-m
y=-2x+4=0
x=2
So - M = 2
m=-2

Given that the intersection of the line y = 3x + m and the line y = 4-2x is on the x-axis, the value of M is obtained

The intersection of the line y = 3x + m and the line y = 4-2x is on the X axis (that is, when y = 0, the value of X is the same)
3x+m=4-2x=0,x=2
m=-5x+4
=-5*2+4
=-6

Y = - 2x + 8 and X axis intersect with point P, translation line y = 3x, make it pass through point P, find the expression of the line after translation
Trouble

Y = 0 on X-axis
y=-2x+8=0\
x=4
So p (4,0)
In translation, the coefficient of X remains unchanged
So it's y = 3x + B
Over P
0=3×4+b
b=-12
So it's y = 3x-12

The line y = 2x = 8 and the x-axis are called at the point P. translate the line y = 3x so that it passes through the point P. find the expression of the line after translation
also:
When x increases gradually from 0, whose value is greater than 20 first compared with y = 2x-6 and y = 1 / 2x?

1.y=2x+8=0,x=-4
Y = 2x + 8 and X axis intersect at (- 4,0),
Let the translation line be y = 3x + B, then (- 4,0) is substituted into
0=3*(-4)+b
b=12
So the line is y = 3x + 12
2.2x-6=20,x=13
x/2=20,x=40
So y = 2x-6 is greater than 20 first

It is known that the function f (x) defined on R satisfies: for any real number a, B, there is always f (a + b) = f (a) + F (b) (1) Find f (0); (2) judge the parity of F (x). (3) if x > 0, f (x) > 0. Judge the monotonicity of F (x). And give the proof