1. Let f (1-x / 1 + x) = x, then the expression of F (x) is: 2. Given the quadratic function f (x) = x2 + X + a (a > 0), if f (m)

1. Let f (1-x / 1 + x) = x, then the expression of F (x) is: 2. Given the quadratic function f (x) = x2 + X + a (a > 0), if f (m)

Question 1: (1-x) / (1 + x) = 2 / (x + 1) - 1 ①
1/①+1=1/2/（x+1)=（x+1）/2…… ②
② * 2-1 = x, so take (1-x) / (1 + x) as an X
That is 1 / (x + 1) * 2-1 = 2 / (x + 1) - 1 = (2-x-1) / (x + 1) = (1-x) / (1 + x) = f (x)
The second question: from m ^ 2 + m + A0, so Δ = (1-4a) / 4 = 0.25-a > 0  0

We know the function f (x) = 2x + 2-x. (1) judge the parity of the function; (2) find the monotone increasing interval of the function and prove it

(1) The definition domain of function f (x) is r, f (- x) = 2-x + 2x = f (x); 〈 f (x) is even function; (2) f ′ (x) = 2xln2-2-xln2 = LN2 (2x-2-x); 2x ≥ 2-x, that is, when x ≥ - x, X ≥ 0, f ′ (x) ≥ 0; 〈 f (x) increases monotonically on [0, + ∞), and [0, + ∞) is the monotone increasing interval of F (x)

① Given a = [- 1,3), B = (0, + ∞), find a ∩ B, a ∪ B
② Let the complete set be r, set a = [- 1,3), set B = (0, + ∞), find the complement of a and the intersection of a and B
③ Given set a = [- 1, + ∞), set B = (0, + ∞), find a ∩ B, a ∪ B
Try to complete the process so that I can understand it

1.A∩B=(0,3),A∪B=(-1,+∞)
2. The complement of a = (- ∞, - 1) ∪ [3, + ∞),
Intersection of complements of a and B = = (- ∞, - 1)
3.A∩B=(0,+∞)
A∪B=[-1,+∞）