It is known that the function f (x) defined on [0,1] satisfies the following three conditions simultaneously It is known that the function f (x) defined on [0,1] satisfies the following condition: when x1 ≥ 0, X2 ≥ 0, X1 + x2 ≤ 1, f (x1 + x2) ≥ f (x1) + F (x2) always holds, and whether the function g (x) = 2 ^ X - 1 satisfies this condition in the interval [0.1]

It is known that the function f (x) defined on [0,1] satisfies the following three conditions simultaneously It is known that the function f (x) defined on [0,1] satisfies the following condition: when x1 ≥ 0, X2 ≥ 0, X1 + x2 ≤ 1, f (x1 + x2) ≥ f (x1) + F (x2) always holds, and whether the function g (x) = 2 ^ X - 1 satisfies this condition in the interval [0.1]

Let's test the hypothesis
f(x1+x2)=x1^2+x2^2-2*x1*x2-1
f(x1)=x1^2-1,f(x2)=x2^2-1
By substituting f (x1 + x2) > = f (x1) + F (x2)
1 + 2 * X1 * x2 > = 0 is obviously proved by X1 > = 0, X2 > = 0
Therefore, the conditions are satisfied
Hope to adopt, thank you!

Given the function f (x) = LG [a (A-1) + x-x & # 178;] (a ≠ 1 / 2), find the domain of definition a?

If the domain is a (A-1) + x-x ^ 2 > 0, the solution of the inequality is the domain
(a-x)(a-1+x)>0
When (x-a) (x-1 + a) 1 / 2, the solution is 1-A

Given the function f (x) = 2 / X & # 178; + LG (x + √ 1 + X & # 178;), and f (- 1) ≈ 1.62, then f (1) ≈?

Let f (x) = f (x) - 2 / x ^ 2 = LG (x + √ 1 + X & # 178;)
We obtain that f (x) is an odd function
So f (1) = - f (- 1)
So f (1) - 2 = - (f (- 1) - 2)
The results show that f (1) = 4-f (- 1) = 2.38

Find the function f (x) = LG (X & # 178; - 1) + 8 and f (x) = e ^ (x-1) - 4
Finding zero point

The solution requires the zero point of F (x), that is, f (x) = 0, so we get x ^ 2-1 = 1, x ^ 2 = 2, x = positive and negative root sign 2, so the zero point of F (x) is x = positive and negative root sign 2,
Similarly, we get that e ^ (x-1) = 4, so X-1 = ln 4, that is, x = ln 4 + 1, so the zero point of F (x) is x = ln 4 + 1
Note that the zero point of a function is a value, not the coordinates of a point