A high school on the concept of function to understand the problem Why should we pay attention to the change of the value range of the independent variable when we use the substitution method in the method of finding the analytic expression of a function, otherwise we may not get the incorrect result?

A high school on the concept of function to understand the problem Why should we pay attention to the change of the value range of the independent variable when we use the substitution method in the method of finding the analytic expression of a function, otherwise we may not get the incorrect result?

For example, let 2 ^ x = t, because 2 ^ x is ＞ 0, so t is also ＞ 0. If the scope is not limited, the possible solution of T in the later solution will be ＜ 0, it should be deleted

The definition of high school function is as follows:
Let a and B be two sets of nonempty numbers. If, according to a certain correspondence F, there is a unique definite number f (x) corresponding to any number x in set a, then f: a → B is a function from set a to set B. denote y = f (x), X ∈ a
I feel that f (x) appears abruptly. I think it's better to define it as follows:
Let a and B be two sets of nonempty numbers. If, according to a certain corresponding relation F, there is a unique number y corresponding to any number x in set a in set B, then f: a → B is a function from set a to set B, denoted as y = f (x), x ∈ a
In this way, the appearance of F (x) is very natural

Yes, your description is close to the definition of function in junior high school textbooks, which is conducive to the acceptance of senior high school freshmen. Although the meaning is the same, it is easier to accept. Very good change

The concept of high school function

Let a and B be nonempty sets of numbers. If, according to a certain corresponding relation F, there is a unique and definite number f (x) corresponding to any number x in a set B, then f: a → B is a function from a set a to B

High school function problem, please specify the steps to solve the problem
If f (x) = (x ^ 2) + LG (under x + root (1 + x ^ 2)), and f (2) = 3, then f (- 2) =?

If x = 2, f (x) = 4 + LG (2 + root (5)) = 3, then LG (m) = - 1 = = > 0

Given curve C: y = ax ^ 2 + BX + C, where a > b > C, a + B + C = 0
The length of the line segment of the curve C cut by the x-axis is L

If a ≤ 0, then 0 ＞ B ＞ C, a + B + C ＜ 0 does not hold, so a ＞ 0. And a + B + C = 0, we get C ＜ 0. Let y = 0, we get ax & # 178; + BX + C = 0. From WIDA's theorem, we get X1 + x2 = - B / A, x1x2 = C / A. thus, l = | x1-x2 | = √ (x1-x2) &# 178; = √ ((x1 + x2) &# 178; - 4x1x2) = √ ((B & # 178; - 4ac) / A & # 178

Given the function f (x) = alnx-2ax + 3 (a ≠ 0). (I) let a = - 1, find the extremum of function f (x); (II) under the condition of (I), if the function g (x) = 13x3 + X2F '(x) + M] (where f' (x) is the derivative of F (x)) is not a monotone 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 The monotone decreasing interval of (2 points) f (x) is (0,12), and the monotone increasing interval is (12, + ∞) & nbsp; & nbsp; & nbsp; & nbsp The minimum value of F (x) is f (12) = − ln12 + 2 × 12 + 3

It is known that f (x) = 2x + BX + 1 of a (a, B are constants, AB is not equal to 2), and f (x) f (1 of x) = K (constant)
1. Finding the value of K
2. If f (f (1)) = 2 / K, find the value of a and B

Given the function f (n) = 1, n = 0n · f (n − 1), n ∈ n *, then the value of F (6) is ()
A. 6B. 24C. 120D. 720

∵f(n)＝1，n＝0n•f(n−1)，n∈N*，∴f（6）=6•f（5）=6•5•f（4）=6•5•4•f（3）=6•5•4•3•f（2）=6•5•4•3•2•f（1）=6•5•4•3•2•1•f（0）=6•5•4•3•2•1•1=6！ =720 selected D

If f (x + 1 / x) = x ^ 2 + x ^ 2 / 1 find y = f (x) analytic formula (2) if f (2 / x + 1) = lgx find y = f (x) analytic formula if you can, the foundation is not very good

In the first question, the integral formula is (x + 1 / x), and the equal sign is written as (x + 1 / x) ^ 2-2. Replace the original formula with the integral, and then replace the whole with X. f (x) = x ^ 2-1. In the second question, the whole is (2 / x + 1). Let the whole be represented by T, then x = 2 / (t-1), Just bring it to the end of the equal sign. This is the way to understand and solve

It is difficult to solve the equation
X + 2 power of 3-2-x power of 3 = 80
Find the value of X

It's very simple. X + 2 of 3 is x times of 9 * 3, and then change the element