![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
The function f (x) = x / (AX + b) (a, B are non-zero real constants) satisfies that f (2) = 1 and the equation f (x) = x has only one solution 1. Find the value of a and B. We already know that a = 0.5, B = 1 2. Is there a real constant M, n such that for any x, f (x) + F (M-X) = n constant in the domain of definition? If so, find out the value of M, N. if not, explain the reason
（2）f（x）=2x/（x+2）
f（x）＋f（m－x）
=2x/（x+2）＋2（m-x）/（m-x+2）
=n
Let x = 0, then 2m / (M + 2) = n
Let x = - 1, then 2 (M + 1) / (M + 3) = n + 2
The solution is: M = - 4, n = 4
∴f（x）+f（-x-4）
=2x/（x+2）+2（x+4）/（x+2）
=4
RELATED INFORMATIONS
- 1. The function f (x) is differentiable on [0,1] and 0
- 2. Let f (x) be differentiable on [0,1] and 0
- 3. For any differentiable function f (x) on R, if x is not equal to 1 and satisfies (x-1) f '(x) > 0, it is proved that f (0) + F (2) > 2F (1)
- 4. It is proved that if the function f (x) is a strictly increasing function on [a, b], then the equation f (x) = 0 has at most one real root on the interval [a, b]
- 5. It is known that the domain of F (x) is r, and its derivative satisfies 0
- 6. Given that the function defined on (0, -∞) satisfies f (x, y) = f (x) + F (y), and if x > 1, f (x) < 0, if f (half) = 1, find the solution set of the inequality f (x) + F (5-x) ≥ - 2 Is f (XY) = f (x) + F (y)
- 7. 5. Given that f (x) is an odd function defined on R, when x ≥ 0, f (x) = x-2x, find the expression of F (x) on R 5. Given that f (x) is an odd function defined on R, when x ≥ 0, f (x) = x-2x, find the expression of F (x) on R 6. It is known that the function f (x) is an even function on R. when x ≥ 0, f (x) = x-2x-3 (1) Write the expression of function y = f (x) with piecewise function; (2) Using symmetry to draw its image; (3) The monotone interval is pointed out; (4) It is pointed out that in what interval f (x) > 0 and in what interval f (x) < 0 by using images; (5) Find the maximum value of the function 7. Find the range of function y = 1 / X (x ＞ - 4 and X is not equal to 0) 8. Find the range and monotone interval of the function y = | x + 2 | - | X-5 | 9. It is known that the function y = f (x) is an even function defined on R. when x < 0, f (x) is monotonically increasing. The solution set of the inequality f (x + 1) > F (1-2x) is obtained 10. The definition field of function y = x-3x-4 is [0, M], the range of value is [- 25, 4, - 4], and the value range of real number m is obtained
- 8. It is known that y = f (x) is an odd function defined on R. when x ≥ 0, f (x) = x2-2x, then the expression of F (x) on R is () A. -x（x-2）B. x（|x|-2）C. |x|（x-2）D. |x|（|x|-2）
- 9. It is known that f (x) is an odd function defined on R. when x > 0, f (x) = x ^ 2-2x + 1, then the expression of F (x) is Its function-
- 10. When X & gt; 0, FX = - x + 1, then when X & gt; 0, the expression of FX is?
- 11. Given that the function f (x) = x divided by ax + B (a, B is constant and a ≠ 0) satisfies f (2) = 1, the equation f (x) = x has a unique solution, find the function f (x) And find the value of F (f (- 3))
- 12. Given the function f (x) = x2ax + B (a, B are constants) and the equation f (x) - x + 12 = 0 has two real roots X1 = 3, X2 = 4. (1) find the analytic expression of function f (x); (2) let k > 1, solve the inequality about X; f (x) ＜ (K + 1) x-k2-x
- 13. If f (x) is an odd function on R, and the period of F (2x-1) is 4, if f (6) = - 2, then f (2008) + F (2010)=______ ．
- 14. If f (x) is an odd function with period 4, and f (- 1) = a, (a ≠ 0), then the value of F (5) is equal to
- 15. If f (x) is an odd function with period of 2 Π and f (- Π / 2) = - 1, then what is f (5 / 2 Π) equal to
- 16. Given that the function f (x) = log (1-mx) / (x-1) is an odd function in the domain of definition, find m and its domain of definition
- 17. Let f (x) = Log1 / 2 (10 ax), where a is a constant, f (3) = - 2, KKK Let f (x) = Log1 / 2 (10 ax), where a is a constant and f (3) = - 2 (1) The value of a (2) If for any x ∈ [3,4], the inequality f (x) ＞ (1 / 2) ^ x + m, find the value range of real number M
- 18. Given the function f (x) = log2 (1 + x) / (1-x), prove f (x1) + F (x2) = f ((x1 + x2) / (1 + x1x2))
- 19. Given the function f (x) = LNX ax. (1) when a > 0, judge the monotonicity of F (x) in the domain of definition; (2) if the minimum value of F (x) in [1, e] is 32, find the value of A
- 20. Given that the image of the function f (x) = a ^ x + m passes through the point (1,7), and the image of his inverse function y = f ^ (- 1) passes through the point (4,0), find the value of a, M