Why can any function defined by a symmetric interval be expressed as the sum of an even function and an odd function

Any function f (x), construct two functions, G (x), H (x), where g (x) = (f (x) - f (- x)) / 2 h (x) = (f (x) + F (- x)) / 2 because g (- x) = (f (- x) - f (x)) / 2 = - G (- x) H (- x) = (f (- x) + F (x)) / 2 = H (x), G (x) is odd function, H (x) is even function, G (x) + H (x) = (f (x) - f (- x)) / 2 + (f (x) = (f (x) = (f (x) - f (- x)) / 2 + (f (x) = (f (x) = (f (x) = (f (x) = (f (x) =

RELATED INFORMATIONS

1. Let y = f (x) (x ∈ R and X ≠ 0) be f (XY) = f (x) + F (y) for any nonzero real number x, y (1) Verification: F (1) = f (_ 1) And f (1 / x) = - f (x) (x ≠ 0) (2) judge the parity of F (x) (3) if f (x) monotonically increases on (0, + ∞), solve the inequality f (1 / x) - f (2x-1) ≥ 0
2. If XY is a real number and the square of x = the square of Y, then
3. Compare the size of x2-xy + Y2 and X + Y-1 Step by step,
4. If XY is a real number and M = 3x ^ 2 + 2Y ^ 2-2xy-4x-2y-3, determine the minimum value of M!
5. 4x^3y+4x^2y^2+xy^2
6. Known (X-Y) (x ^ 2 + XY + y ^ 2) = x ^ 3-y ^ 3 1. If A-B = 4, a ^ 3-B ^ 3 = 28, find a ^ 2 + AB + B ^ 2 2. Factorization m ^ 3-N ^ 3 + N-M
7. It is known that XY + x = - 3, xy-y = 2 Find the value of the algebraic formula - X - [2y-2 (XY + x) ^ 2 + 3x] + 2 [x + (xy-y) ^ 2]
8. We know that x + y = 3, xy = - 12, x ^ 2-xy + y ^ 2
9. Calculate 3xy [2xy-x (Y-2) + X-1]
10. X ^ y times (2xy-3xy ^ 2)=___________________ =________________
11. What's the difference between even function and odd function
12. Is f (x) = 0 the only function that is both odd and even? Except for other function forms with different domain!
13. It is known that f (x) is an even function and an increasing function on (0, + ∞) It is known that f (x) is an even function and is an increasing function on (0, + ∞). It is proved that f (x) is an increasing function or a decreasing function on (- ∞, 0)
14. What are the characteristics of the domains of odd and even functions
15. We know that FX = x square + (a + 1) + a square, if FX can be expressed as the sum of an odd function GX and an even function HX (1) Find the analytic expressions of GX and HX. (2) if FX and GX are decreasing functions in the interval (- ∞), (a + 1) square), find the value range of F1
16. Given the function FX = 2 ^ X and FX = GX + HX, where GX is an odd function and HX is an even function, if the inequality 2A * GX + H (2x) ≥ 0 holds for any x ∈ [1,2], Then the value range of real number a is
17. If f (x) is an even function, G (x) is an odd function, and f (x) + G (x) = x2 + X-2, find the analytic expressions of F (x) and G (x)
18. FX GX = x ^ 2-x, FX is odd function, GX is even function, find FX
19. Given that F X is an odd function, G x is an even function and f (x) - Gx = x2 + 3x + 2, then FX + Gx =?
20. The odd function FX and even function GX satisfy the following conditions: FX + Gx = x sub dense of a, - x sub dense of a + 2A > 0 Not equal to 1, if G2 = a find F2