Positive and negative of exponential function What does it mean that the same value of the bottom truth is positive and the different value of the bottom truth is negative

Positive and negative of exponential function What does it mean that the same value of the bottom truth is positive and the different value of the bottom truth is negative

If the base real number is greater than one or greater than zero and less than one at the same time, the value is positive
The real number of the base is greater than one, greater than zero and less than one, and the value is negative

Given that the domain of F (x) is {x I x belongs to R and X is not equal to 0} and satisfies 2F (x) - 1 / x = f (1 / x), then what is the minimum value of F (x)?

First, the analytic expression of F (x) is solved
Let t = 1 / X
That is 2F (1 / T) - t = f (T)
That is, 2f (1 / x) -x = f (x), and the analytical expression of F (x) is obtained simultaneously with the original expression
That is, f (x) = (︱ x + 2 / ︱ x) / 3. The minimum value of F (x) can be calculated by using important inequalities
(2√2)/3

How to find the maximum and minimum of exponential function

In senior high school, we will calculate the derivative function once, make it equal to zero, and then bring two values or one value into the original function for evaluation, and then bring the two ends of the interval into the original function for calculation. We will know the maximum and minimum by comparing the four values
If the above is a general exponential function, it will be written automatically. You don't need to seek the derivative, it should be monotonic. You just need to bring in the two ends of the domain for comparison

Let: P: exponential function y = ax monotonically decrease in R; Q: curve y = x2 + (2a-3) x + 1 intersects with X axis at two different points. If P ∨ q is true, ￢ q is also true, the value range of a is obtained

∵ when 0 ＜ a ＜ 1, the exponential function y = ax decreases monotonically in R, when a ＞ 1, the exponential function y = ax increases monotonically in R, ∵ when proposition p is true, 0 ＜ a ＜ 1; when proposition p is false, a ＞ 1. ∵ there are two different intersections between the curve y = x2 + (2a-3) x + 1 and the X axis, which are equivalent to (2a-3) 2-4 ＞ 0