If x ∈ R, f (x) satisfies f (XY) = f (x) + F (y), how to prove that f (x) is an even function?

If x ∈ R, f (x) satisfies f (XY) = f (x) + F (y), how to prove that f (x) is an even function?

Let x = 1, y = 1, f (1) = f (1) + F (1) = 2F (1), so f (1) = 0
X = - 1, y = - 1, then f (1) = 2F (- 1), so f (- 1) = 0
Let y = - 1, then f (- x) = f (x) + F (- 1) = f (x),
That is, f (x) = f (- x)
So f (x) is an even function

The function y = 2x2-8x + 1, when x=______ The maximum value of Y is 0______ Value equals______ ．

When x = - B2A = - - 82 × 2 = 2, there is a minimum value = 4ac − b24a = 4 × 2 × 1 − (− 8) 24 × 2 = - 7

What is the main content of space-time in Einstein's special theory of relativity

The measurement results of time and space are different in different reference frames. The moving clock will slow down, the moving rod will shorten, and the mass of the moving object will increase. The speed of light is the same in all reference frames, and the speed of light is the highest. This is the content of special relativity

A piece of rectangular cardboard is 8 cm long and 6 cm wide. If you fold it into the side of a rectangle with a square bottom, how many square centimeters is the bottom area of the rectangle?

8 △ 4 = 2 (CM) 6 △ 4 = 1.5 (CM) 2 × 2 = 4 (square cm) 1.5 × 1.5 = 2.25 (square cm) a: the bottom area of the cuboid is 4 square cm or 2.25 square cm

It is known that a sinusoidal electromotive force is e = 311sin (314T) v?

The maximum value is 311, the effective value is 311 / (root 2), the frequency is 314, the period is (2pai / 314), and the initial phase is 0

A cuboid tin oil tank is 80cm long, and its cross section is a square with a side length of 50cm. (1) ignoring the joint, how much tin is needed to make this oil tank? (2) Regardless of thickness, how many liters of gasoline can this tank hold?

(1) 80 × 50 × 4 + 50 × 50 × 2 = 16000 + 5000 = 21000 (square centimeter); answer: this oil tank needs 21000 square centimeter iron sheet. (2) 80 × 50 × 50 = 200000 (cubic centimeter), 200000 cubic centimeter = 200 liter; answer: this oil tank can hold 200 liter gasoline at most

I want something about, for example, the area of a rectangle equals length times width

1. There is only one straight line passing through two points. 2. The shortest line segment between two points. 3. The complementary angles of the same angle or equal angle are equal. 4. The complementary angles of the same angle or equal angle are equal. 5. There is only one straight line passing through one point and the known straight line is perpendicular. 6. Among all the line segments connected by a point outside the straight line and the points on the line, the shortest vertical line segment is 7

If the circumference of the bottom surface of the cone is 20 π, and the center angle of the sector is 120 ° after the side expansion, then the side area of the cone is?

The radius of the circle where the fan-shaped cone is developed on the side is r, the circumference of the cone bottom is the arc length of the fan-shaped cone developed on the side, and the arc length of the fan-shaped cone is 1 / 3 of the circumference length, so r = 30 can be obtained. The area of the cone side, that is, the area of the fan-shaped circle, is 1 / 3 π R * r = 300 π

In division with remainder, the divisor=______ ．

Divisor = quotient × divisor + remainder. So the answer is quotient × divisor + remainder

The sum of the circumference and diameter of a circle is 20.7 meters. How many square meters is the area of the circle? (π = 3.14)

π D + D = 20.7 (π + 1) d = 20.7 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; d = 20.7 △ 4.14 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; d = 5 the area of the circle is: 3.14 × (5 △ 2) 2 = 19.625 (square meters) a: the area of the circle is 19.625 square meters