Solving function analytic expression by equation method Given that f (x) satisfies 2F (x) + F (1 / x) = 3x, find f (x) I don't understand why f (x) = 3 / x-2f (1 / x),

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• 1. The elimination method of solving function in senior one If f (x) satisfies the equation AF (x) + F (1 / x) = ax, X ∈ R, X ≠ 0, a is a constant, a ≠± 1, then f (x)=__ Solution: using the elimination method ∵ AF (x) + F (1 / x) = ax If x is replaced by 1 / x, then 1 / X is replaced by X The following is omitted I just want to ask why it can be converted That's not waiting After the transformation, a system of equations is formed with the first equation. I'll try again. It can't be solved at all. I'm looking for advice from experts.
• 2. The fixed cost of producing a certain product in a factory is 20 million yuan, and the cost increases by 100000 yuan for each unit of product. We also know that the total revenue K is a function of the number of unit products Q, and K (q) = 40q-120q2, then the maximum value of total profit L (q) is______ ．
• 3. The problem of function representation 1. Given that the quadratic function f (x) satisfies f (x + 2) - f (x) = 4x + 6 and f (0) = 1, find the analytic expression of F (x) 2. Let f (x) = x / (x ^ 2 + 1), then f (1 / x) equals 3. Let y = (m-1) x ^ (m ^ 2 + m) + MX + 3 be a quadratic function with independent variable x, then M= 4. Given that the function y = f (x) satisfies f (x) = 2F (1 / x) + X, find the analytic formula of F (x) 5. Find the first-order function f (x) so that f {f [f (x)]} = 8x + 7 The solution is similar: F (f (x)) = 4x-1 f(x)=x (there is no need to find out the exact value of x)
• 4. 1. If one root of the equation x & sup2; - (A & sup2; - 1) x + (A-2) = is larger than 1, and the other root is larger than 1, then the value range of a is____ . 2. If the function f (x) = MX & sup2; + (2m-1) X-2 has at least one zero point, then the value range of M_________ .
• 5. In mathematics of grade one of senior high school, the root of equation and the zero point of function Using the image of the function, the approximate interval of the zeros of the following functions is pointed out (1) F (x) = the third power of negative x + 3x + 5; (2) F (x) = the (R-1) power of E + 4x-4; Please help me. I can't type some symbols. Thank you~ Just talk about how to do it. Thank you
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• 9. The concept of function is not very clear. Please explain it in detail For example, f (2x + 1) = x + X What are x and 2x + 1 in brackets and what is X after equal sign
• 10. Let a and B be a set of nonempty numbers, and F: X → y be a corresponding rule from a to B. then the mapping f: a → B from a to B is called a function, denoted as y = f (x), where x ∈ a, y ∈ B, the original image set a is called the definition field of function f (x), and the image set C is called the value field of function f (x). Obviously, there is C ∈ B Why is it that the elements in the image set C ∈ B, not to say that B is the range of the function f (x), can remain?
• 11. Senior one mathematics [function & equation] Given that the two equations x ^ 2 + BX + 1 = 0 are α, β (α ≠ β), then the two equations x ^ 2 + (b-2) X-B are_________ .
• 12. Solving function analytic expression by function equation method f（x）+f(3x)=3x What is the basis of F (3x) + F (x) = x
• 13. The solution of analytic formula of higher one function F (x + 1) = x-3x + 2
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• 15. Who can help me with this problem It is known that if the inverse scale function of points a (4, m) and B (- 1, n) is y = 8 / X on the image, if point D is on the Y axis and Da = dB, (1) find the coordinates of two points a and B; (2) find the coordinates of point D emergency
• 16. Simple secondary function problem. Do me a favor~ Known parabola y = - 2x ^ 2-3 When x_______ Y increases with the increase of X; When x_______ Y decreases with the increase of X Then why can't we say it is: When x ≤ 0, y increases with the increase of X; When x ≥ 0, y decreases with the increase of X? That's why we can't include "0"?
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• 19. (1) Given that the definition field of function f (x) = LG (a (the square of x) + ax + 1) is r, the value range of real number a is obtained; (2) given that the value range of function f (x) = LG (a (the square of x) + ax + 1) is r, the value range of real number a is obtained;
• 20. Given that f (√ x + 1) = x + 2 √ x, try to determine the analytic formula F (x) Why can the number of substitution be directly converted to x?