The function f (x) = 3 ^ (2x) - (K + 1) * 3 ^ x + 2, when f (x) is always greater than zero, the value range of K is obtained One is the method of quadratic function, more troublesome, there is another method, forget what the principle is, please help Why is Δ wrong? 2√2-1）

The function f (x) = 3 ^ (2x) - (K + 1) * 3 ^ x + 2, when f (x) is always greater than zero, the value range of K is obtained One is the method of quadratic function, more troublesome, there is another method, forget what the principle is, please help Why is Δ wrong? 2√2-1）

Let t = 3 ^ x, then t > 0,
Then f (x) = T & sup2; - (K + 1) t + 2
If x belongs to R, f (x) is always positive
Then T & sup2; - (K + 1) t + 2 > 0 holds,
That is: T & sup2; + 2 ＞ (K + 1) t
∴（t² + 2)/t ＞ k + 1
So K < T + 2 / T - 1
For T + 2 / T,
When t = √ 2, t + 2 / T has a minimum value of 2 √ 2
When k is less than the minimum value of T + 2 / T - 1, the original formula holds,
∴k ＜2√2 - 1

Function problem (should be very simple)
It is known that the area of a rectangle is 20 square centimeters, and the length of one side is x centimeters. Find the function analytic formula of the adjacent side length y (CM) with respect to X (CM), and write out the domain of definition of this function
Is it 0 < x ≤ 20 or x > 0

Y = 20 △ X domain 0 ＜ x ≤ 20

On function (very simple)
F (x / 2) = 1 / 4x ^ 2-x for f (x)
How to solve this kind of problem

Let t be equal to all the parts in the brackets of the function f (), for example, let t be equal to all the parts in the bracket of the function f (). In this case, we get a function about t and X, and then use t to express x, that is, to solve the value of X. in this case, x = 2T satisfies f (x / 2) = 1 / 4x ^ 2-x, so we bring x = 2T in and get f (T) = 1

A function problem
The quadratic function f (x) = ax ^ 2 + BX + C (a > 0) is known if f (c) = 0 and 0
I think it's a bit difficult, too

If f (c) = 0, and 00 1, f (c) = AC & sup2; + BC + C = C (AC + B + 1) = 0, ∵ 00, the solution is B0, then both sides of the inequality are multiplied by X (x + 1) (x + 2) and reduced to: (a + B + C) x & sup2; + (a + 2B + 3C) x + 2C > 0; f (1) = a + B + C > 0, then as long as Δ = (a + 2B + 3C

Finding the analytic expression of function
Given f (1 + 1 / x) = 1 / (x ^ 2) - 1, find f (x)

Let 1 + 1 / x = t 1 / x = T-1 not equal to 0, so t is not equal to 1
f(t)=(t-1)^2-1=t^2-2t
f(x)=x^2-2x （x≠1）

I can't remember how to write it at the moment
The fruit grower first sells some pineapples at a certain price, and then sells all the remaining pineapples at a lower price. The tonnage of pineapples sold X and the price of his income y (ten thousand yuan)
What is the price per kilogram of pineapple before the price reduction?
If the price of pineapple is 1.6 yuan, his total income is 20000 yuan. How many tons of pineapple did he buy?
There is a function image, the horizontal axis is x tons, the vertical axis is y 10000 yuan, the first point is (8,1.92), the point after the price reduction is (x, 2)

1 19200 divided by 8000 equals 2.4 yuan per kilogram
20000 divided by 1.6 equals 12500 kg, which is 12.5 tons

Let even function f (x) satisfy: F (x) = x & # 179; - 8 (x ≥ 0), and find the function relation when x ≤ 0
F (x) = - X & # 179; - 8 but I won't prove it, please prove it

When x ≤ 0,
f(-x)=(-x)³-8=-x³-8
∵ f (x) is an even function
∴f(x)=f(-x)=-x³-8

sweat
Letter quality m / G 0

Of course, a function is the relationship between several numbers. As long as there is a relationship, a certain number is the function of another or several numbers. A function may not be expressed by a mathematical formula
The above problem can be expressed by piecewise function and different formulas when the independent variables are in different intervals
y={0.8 (0

Well
How to find the range of y = x + 1 / x? How to find the monotone interval? Besides drawing, is there an algebraic method?
There is another problem: if the odd function f (x) is x ∈ [0, + ∞), f (x) = x (1-x), then if x ∈ (- ∞, 0), f (x)=__________

1. Y=X+1/X
Range (- ∞, - 2] u [2, + ∞)
Monotone interval (- ∞, - 1] u [1, + ∞) monotone increasing [- 1,0) U (0,1] monotone decreasing
The simplest way to draw a picture is in quadrant one or three. Otherwise, we need to use derivative
2.f(x)=-x(1+x)

What does x represent? Are the Algebras in brackets the same in F (2x + 2) and f (x)?

X represents the number in a set, and f (x) is the mapping set of numbers in X
The algebra in brackets of F (2x + 2) and f (x), if x is the same and the value range is real, then the image of F (x) is the same, but it is different from the relative position of X and Y axes
If x is the same, and the value range is different, then f (2x + 2) and f (x) are very likely to be different