Solving function analytic expression by function equation method f（x）+f(3x)=3x What is the basis of F (3x) + F (x) = x

RELATED INFORMATIONS

• 1. 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_________ .
• 2. 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),
• 3. 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.
• 4. 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______ ．
• 5. 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)
• 6. 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_________ .
• 7. 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
• 8. How to find the number of zeros of a function Be specific
• 9. Approximate solution of equation by dichotomy
• 10. Roots of equations and zeros of functions Given the power of function f (x) = 3 to the power of X - the power of X... Ask if the equation f (x) = 0 has a real root in the interval [- 1,0]? Why? Some symbols can't be typed. Please give me a general solution,
• 11. The solution of analytic formula of higher one function F (x + 1) = x-3x + 2
• 12. Two methods of solving function For example, f (x + 1) = x ^ 2, how does f (x) = (x + 1) ^ 2-2 (x + 1) + 1 come from
• 13. 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
• 14. 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"?
• 15. Function problem, do me a favor Is y = 3 a positive proportional function? Explain why
• 16. If AB + C = Ba + C = Ca + B = k, then the line y = KX + 2K must pass () A. Quadrant 1 and 2 b. quadrant 2 and 3 C. quadrant 3 and 4 d. quadrant 1 and 4
• 17. (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;
• 18. 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?
• 19. 1. If the domain of definition of function f (x) = quadratic radical (AX + 2) is (- ∞, 1], find the real number a 2. If the function f (x) = quadratic root sign (AX + 2) is significant in (- ∞, 1], find the real number a 3. If the domain of definition of function f (x) = quadratic root (AX & sup2; + BX + C) is [1,3], find the domain of definition of function f (x) = quadratic root (BX & sup2; - ax + C) I don't understand very well. It's better to have explanation and steps,
• 20. In order to know three points a (1,2), B (4,1), C (3,4), take a point P on the line AB so that the line PQ passing through P and parallel to BC divides the triangle ABC into two parts: the triangle Apq and the quadrilateral pqcb, and their area ratio is s Triangle APQ:S Quadrilateral pqcb = 4:5, find the coordinates of point P There is no picture for this problem. I have to draw it myself. But I don't know how to do it. I want to get the process.