Known function f (x) = a INX + x ^ 2 (a is a real constant) (1) If a = - 2, prove that f (x) is an increasing function on (1, positive infinity); (2) find the minimum value of the function on [1, e] and the corresponding x value; (3) if x belongs to [1, e] so that f (x) is less than or equal to (a + 2) x, please try not to use special symbols to find the value range of real number a,

Known function f (x) = a INX + x ^ 2 (a is a real constant) (1) If a = - 2, prove that f (x) is an increasing function on (1, positive infinity); (2) find the minimum value of the function on [1, e] and the corresponding x value; (3) if x belongs to [1, e] so that f (x) is less than or equal to (a + 2) x, please try not to use special symbols to find the value range of real number a,

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Let a be a positive constant, f (x) = | ax-x2 | + INX, weak a = 2, find the monotone interval of the function

The original function is transformed into f (x) = x (2-x) + LNX
The domain is x > 0 when x > 2
f(x)=x(x-2)+lnx
Derivative = X-2 + X + 1 / x = 2x ^ 2-2x + 1
Because Δ 0, the value of the function is always positive
So when x > 2, the function monotonically increases but not decreases
When 0

Given that f (x) is an even function on R, and f (1-x) = f (1 + x), when x ∈ [0,1], f (x) = X2, then y = the number of zeros of F (x) - log7x & nbsp; ()
A. 3B. 4C. 5D. 6

The function f (x) is an even function on R, we can get f (- x) = f (x), f (1-x) = f (1 + x), f (2-x) = f (x), so we can get f (- x) = f (2-x), that is, f (x) = f (X-2), that is, when the period of the function is 2 and X ∈ [0,1], f (x) = x2. To study the number of zeros of the function y = f (x) - log7x, we can transform the problem into several intersections of y = f (x) and y = log7x, as shown in the figure We know that there are six intersections, so we choose D

Let even function f (x) have f (x + 3) = - 1F (x) for any x ∈ R, and if x ∈ [- 3, - 2], f (x) = 4x, then f (107.5) = ()
A. 10B. 110C. -10D. -110

Because f (x + 3) = - 1F (x), there is f (x + 6) = - 1F (x + 3) = - 1 − 1F (x) = f (x). Function f (x) is a function with period 6. F (107.5) = f (6 × 17 + 5.5) = f (5.5) = - 1F (2.5) = - 1F (− 2.5) = - 14 × (− 2.5) = 110