What are the characteristics of the domains of odd and even functions

Their domain of definition is all about
Origin (0,0)
Symmetrical

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1. 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)
2. Is f (x) = 0 the only function that is both odd and even? Except for other function forms with different domain!
3. What's the difference between even function and odd function
4. Why can any function defined by a symmetric interval be expressed as the sum of an even function and an odd function
5. 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
6. If XY is a real number and the square of x = the square of Y, then
7. Compare the size of x2-xy + Y2 and X + Y-1 Step by step,
8. If XY is a real number and M = 3x ^ 2 + 2Y ^ 2-2xy-4x-2y-3, determine the minimum value of M!
9. 4x^3y+4x^2y^2+xy^2
10. 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
11. 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
12. 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
13. 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)
14. FX GX = x ^ 2-x, FX is odd function, GX is even function, find FX
15. Given that F X is an odd function, G x is an even function and f (x) - Gx = x2 + 3x + 2, then FX + Gx =?
16. 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
17. If the function FX is even, the function GX is odd, and FX + Gx = 2x, then FX = GX=
18. FX is an odd function and GX is an even function FX + Gx = x & # - x, then FX=
19. Given the function f (x) = loga [(a ^ x) - 1], a is greater than 1 1. Find the domain of F (x); 2. Find the value of X that holds f (2x) = f ^ - 1 (x)
20. Given the function FX = loga (x + 1) - loga (1-x), a > 0 and a ≠ 1 1. Find the value range of X to make FX > 0