1 find the definition field of log (2x-3) under the function f (x) = root sign 2 given the function f (x) = x square - 4x-7, x [- 4,4], find the value range of F (x)

1 find the definition field of log (2x-3) under the function f (x) = root sign 2 given the function f (x) = x square - 4x-7, x [- 4,4], find the value range of F (x)

1.2x-3>0 x>3/2
2. X = 2 is the symmetry axis of the function, and the function opening is upward. When x = 2, the minimum value is - 11, and when x = - 4, the maximum value is 25

one It is known that the real number m.n satisfies Mn

It is proved that take x1, X2 ∈ (- N / 2, positive infinity) and let x10,2x2 + n > 0f (x1) - f (x2) = (MX1 + 1) / (2x1 + n) - (MX2 + 1) / (2x2 + n) (general points) = (2mx1x2 + mnx1 + 2x2 + n-2mx1x2-mnx2-2x1-n) / (2x1 + n) (2x2 + n) (merge congeners) = (mn-2) (x1-x2) / (2x1 + n) (2x2

The ideas and solutions of the second sub problem of these two questions

Isn't question 15 inserted directly? It's not hard
Question 16, find the axis of symmetry and discuss it in three cases: 1) the axis of symmetry is on the right of 2
2) The axis of symmetry is to the left of 0
3) The axis of symmetry is between [0,2]

The known function f (x) = alnx-2ax + 3 (a ≠ 0) (1) Let a = - 1, find the extreme value of function f (x); (2) Under the condition of (I), if the function g (x) = 1 3x3 + X2F ′ (x) + M] (where f '(x) is the derivative of F (x)) is not a monotonic function in the interval (1,3). Find the value range of real number M

(I) when a = - 1, f (x) = - LNX + 2x + 3 (x > 0), f '(x) = − 1x + 2,... (2 points) ‡ f (x), the monotonic decreasing interval is (0,12) and the monotonic increasing interval is (12, + ∞)     … (4 points), the minimum value of F (x) is f (12) = − ln12 + 2 × 12+3...

Inverse function of finding the square of function y = [(x-1) / (x + 1)] Find the value range of function y = x / (2x + 1) Find the value range of function y = (x-x) / (x-x + 1) If x under the root sign is a real number, find the value range of the function y = x + 3x-5 It is proved by definition that the x power of F (x) = a + the - x power of a is an increasing function on (0, positive infinity), where a > 0 and tangent is not equal to 1

The title is not very difficult, but it is too long to write, and it is difficult to input mathematical symbols. It takes at least half an hour to complete it
Add 20 to more than 50 points. Then someone will answer. What do you say?

1. If the domain of function f (x) is [- 2,1], find the domain of G (x) = f (x) + F (- x) 2. Find the following function range 1)y=2x+1/x-3 2)y=x ²- 4x+6,x∈[1,5) 3. It is known that the function f (x) has f (XY) = f (x) + F (y) for any real number x and Y. find the values of F (0) and f (1)

1. The definition domain of ∵ function f (x) is [- 2,1], that is, f (x) in - 2 ≤ x ≤ 1 ∵ function g (x), f (- x) should also meet - 2 ≤ x ≤ 1, and the solution of - 2 ≤ - x ≤ 1 shows that the definition domain of - 1 ≤ x ≤ 1 ∵ g (x) is [- 1,1] 2.1) when x > 0, there are 2x + 1 / X ≥ 2 √ (2x * 1 / x) = 2 √ 2. At this time, y = 2x + 1 / x-3 ≥ 2 √ 2-3. When x < 0, there are 2x + 1