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The solution of the definition and range of mathematical functions
1. Solution of definition field. (1) if ƒ is an integer, the definition field is R. (2) if ƒ is a fraction, the definition field is all real numbers that make the denominator not zero. (3) if ƒ is an even root, the definition field is all real numbers that make the square number to be opened non negative. (4) if ƒ is a composite function, the definition field
Monotonicity, parity, definition domain and solution of value domain of higher one mathematical function
Network data: 1. Find the analytical formula of the function (1) common methods for finding the analytical formula of the function: ① element exchange method (pay attention to the value range of the new element) ② undetermined coefficient method (known function types such as primary, quadratic function, inverse proportional function, etc.) ③ overall substitution (matching method) ④ construct equations (such as reciprocal of independent variables
Mathematical function representation and value range of senior one On the value range class of function, I hope you can write the idea and process clearly! (1) Let x ∈ (- ∞, + ∞) be the maximum value of function y = 2 / X-1 / - 3 / X / (2) Fold the iron wire with length a into a rectangle, find the functional relationship between the area y of the rectangle and the length x of one side, and find the definition field and value field
The first question is that the functional formula is not standardized and misunderstood
Question 2 (is it so simple to ask?)
y=1/2 (a-2*x)*x (0
The value field of F (x) = │ X-1 │ is [0,1] what is the definition field of F (x)? Y = x + 1 / X (x is not equal to 0 x belongs to R) That is (one in x) y = x + 1 / X (x is not equal to 0, X belongs to R) range
The value range of X-1 is [- 1,1]
The definition field of F [x] is [0,2]
Is it one or two questions
If it's a question
You have to round off 0
Y is 1 + X, y is [1.5, positive infinity)
I'm a junior in high school. I just graduated. You have to believe me
On the value range of higher one mathematical function by separation constant method How to separate, don't give any examples, I want methods,
In the form of y = (AX + b) / (Cx + D), the constant separation method can be used
If the primary term in the molecule is set to t (Cx + D), there is
Y = [t (Cx + D) + M] / (Cx + D) compare with the original fraction to find t and m
Then y = t + m / (Cx + D) is separated
The value range of higher mathematics function and the method of finding the maximum value
The value range is generally obtained by inverse representation, discriminant method and separating variables. The maximum value is obtained by monotonicity
RELATED INFORMATIONS
- 1. 1. The function f (x) defined on R is an odd function, and f (x) = f (2-x). If f (x) is a subtractive function in the interval (1,2), then the function f (x) is a subtractive function in the interval (- 2, - 1)____ Function, in the interval (3,4) is___ Function? (add or subtract) 2. The monotonic decreasing interval of function y = |x ^ 2 + X | is __ I want to know if the numbers - 1 and - 0.5 can be obtained? The answer is yes, but I didn't get it. But I don't think so 3. Given that the value range of function f (x) = 0.75x ^ 2-3x + 4 on interval [a, b] is [a, b], find the values of real numbers a and B
- 2. Questions about the idea of using the definition of definite integral to solve the limit of sequence sum formula or definite integral problem, Which of the following ideas is right when using the definition of definite integral to solve the limit of sum of sequence or definite integral problem? 1. First write down the idea that "it has been verified that this limit exists or meets the existence condition of definite integral"; 2. This kind of problem has recognized limit or definite integral. There is no need to write anything. You can directly use the definition of definite integral to solve it. This idea is also clear (recognized!); 3. Isn't it circular logic to write that assumes existence or not and assumes existence by default? That is, when seeking a value, first assume its existence, and then use the existence to deduce the value, so as to obtain that the assumption is correct, which is similar to proving yourself?
- 3. Several limit problems lin (x^3-3x+2)/(x-1)^2= x->+∞ lin [1/x(sinx)+xsin(1/x)]= x->+∞ Please give the solution process, the more detailed the better, and teach how to find the limit such as 0 / 0 and ∞ / ∞
- 4. Let the function z = x / y. find the total differential dz| (2,1)
- 5. Is the total differential of a binary function the partial derivative?
- 6. If a series of functions have the same analytical formula, the same value range, but different definition fields, these functions are called "homologous functions", and the "homologous functions" with the analytical formula of y = x2 and the value range of {1,4} share () A. 7 B. 8 C. 9 D. 10
- 7. Find the [(2x + 1) / (x-1) power of the definition field and value field F (x) = 3 of the function Because 3 / X-1 belongs to R, all values are not equal to 0 What do you mean? Analyze it in detail and the one behind it
- 8. ★ if the definition field of function f (x + 1) = x ^ 2-2x + 1 is (- 2,0), the decreasing interval of F (x) is ()
- 9. The monotonically decreasing interval of the function f (x) = |logax| (a > 0 and a ≠ 1) is __
- 10. Given the function f (x) = (x ^ 2-x-1 / a) e ^ ax (a > 0) (1) when a = 1, find the monotone interval (2) of function f (x) if the inequality f (x) + 5 / a ≥ 0 vs x ∈ Known function f (x) = (x ^ 2-x-1 / a) e ^ ax (a > 0) (1) When a = 1, find the monotone interval of function f (x) (2) If the inequality f (x) + 5 / a ≥ 0 holds for X ∈ R, find the value range of A
- 11. Known: F (x) + F (13 / 42) = f (1 / 6) + F (1 / 7); Verification: F (x) is a periodic function
- 12. To prove the continuity of the function, can we determine that the function is continuous in the interval as long as we prove the continuity at two endpoints (in the open and closed interval)?
- 13. It is proved that the function f (x) = x2-2x is a monotone decreasing function on the interval (- 1.1)
- 14. Known function f (x) = x2-1 x，x∈（1，2]， (I) judge the monotonicity of F (x) and prove your conclusion by definition; (II) find the range of F (x)
- 15. It is known that the definition domain of function f (x) is (0, + ∞) and satisfies that f (XY) = f (x) + F (y), f (1 / 2) = 1. If 0 < x < y, there is f (x) > F (Y) Solving inequality f (x-3) + F (x + 3) ≥ - 2
- 16. What is the definition field of function f (x) = ln (1-x) + √ (x + 2)? Isn't it [-2,
- 17. What is the domain of the function y = ln (x-1)?
- 18. Proof of higher number function It is proved that the function y = xcosx is unbounded in (0, + infinity), but when x tends to infinity, this function is not infinite
- 19. When people sweat a lot or have severe diarrhea, water and inorganic salts are mainly lost in their blood How to supplement these things`
- 20. Would you please help me explain the meaning of several symbols in this mathematical function? In a quadratic equation AX2 + BX + C = 0 (a > 0) In order to ensure that two different real roots are greater than one, the following requirements shall be met: ① Δ＞ 0 ②f(1)＞0 ③-b/2a＞1 What does f (1) > 0 mean in the second term? Also, how do you understand the whole above?