Given that the function FX satisfies 2F (x) - f (- x) = - x Λ 2 + 4x, then the expression of FX is? | Math enthusiast | Mathematical art

Given that the function FX satisfies 2F (x) - f (- x) = - x Λ 2 + 4x, then the expression of FX is?

Firstly, all x in the equation are replaced by - x, that is, 2f (- x) - f (x) = - x Λ 2-4x is the second expression
Then add the two formulas f (x) + F (- x) = - 2x Λ 2
Then add 3f (x) = - 3x Λ 2 + 4x to the first equation
We obtain f (x) = - x Λ 2 + 4x / 3

RELATED INFORMATIONS

1. Given that the function f (x) satisfies the condition, 2f (- x) + FX = 2x-3 (x belongs to R), find the analytic expression of F (x)
2. It is known that f (x) is a first-order function, which satisfies 3f (x + 1) - 2F (x-1) = 2x = 17
3. Given that the function FX satisfies 3f (x) - 2F (1-x) = 2x + 3, find the analytic formula
4. It is known that the function f (x) is a first-order function and satisfies the formula 3f (x + 1) - 2F (x-1) = 2x + 17 to find the expression of F (x)
5. Finding f (x) by knowing that the function is a linear function and satisfies the relation 3f (x + 1) - 2F (x-1) = 2x-17
6. If we know that f (x) is a linear function and satisfies 3f (x + 1) - 2F (x-1) = 2x + 17, we can find f (x) =?
7. If we know that f (x) is a linear function and satisfies 3f (x + 1) - 2F (x-1) = 2x + 17, then f (x) =? Each step should be described in detail,
8. If we know that f (x) is a function of degree and satisfies 3f (x + 1) = 2x + 17, then f (x) = () A. 23x+5B. 23x+1C. 2x-3D. 2x+5
9. If the function f (x) = a + 2 / 2 ^ X-1 is odd in its domain, then the value of real number a is zero
10. If the function f (x) = a + 2 / (2 ^ x-1) is an odd function in its domain, then the value of the real number a
11. Given that the function F X satisfies FX + 2F (- x) = x3-2, the analytic expression of function F X is obtained More than 50 rewards in 10 minutes
12. If f (x) satisfies 2F (x) - f (- x) = LG (x + 1), X belongs to the problem of (- 1.1) finding f (x)... Finding the analytic formula of function
13. The problem is known 2F (x) + F (1 / x) = 2x, find the analytic expression of F (x)
14. Find the analytic formula of the following functions: (1) if f (2x + 1) = 4x2 + 2x + 1, find the analytic formula of F (x); (2) if 2F (x) - f (- x) = x + 1, find the analytic formula of F (x)
15. Let the derivative function of F [x] on R be f "[x], and 2F [x] + XF" [x] > x ^ 2. Find the size relation of F [x] and X, and the sum of F [x] Suppose that the derivative of F [x] on R is f '' [x], and 2F [x] + XF '' [x] > x ^ 2, find the size relationship between F [x] and X, and the size of F [x] and X That's the title Do it yourself.
16. Given the function f (x) = x2-2ax, find the minimum value g (a) of F (x) in the interval [- 1,1]
17. Given the function f (x) = (2ax-1) / (2x + 1) (1) a = 1, the monotone interval (2) f (x) of F X is the range of increasing function to find a in (negative infinity, - 1 / 2)
18. Given the function FX = x & sup2; - 2aX + 3 (1 ≤ x ≤ 3), find the minimum value H (a) of function FX and write the monotone interval of function H (a)
19. Finding the maximum value of the function FX = x ^ 2-2ax-1 in the interval [0,2]
20. The maximum and minimum values of F (x) = 2x4-3x2 + 1 on [12,2] are______ ．