It is known that the function f (x) whose domain is r decreases monotonically in the interval (- ∞, 5). For any real number T, f (5 + T) = f (5-T), then the following formula must be true () A. f(-1)<f(9)<f(13)B. f(13)<f(9)<f(-1)C. f(9)<f(-1)<f(13)D. f(13)<f(-1)<f(9)
The image of ∵ f (5 + T) = f (5-T) ∵ function f (x) is symmetric with respect to x = 5 ∵ f (- 1) = f (11), ∵ function f (x) decreases monotonically in the interval (- ∞, 5), and ∵ function f (x) increases monotonically in the interval ((∞, 5), + ∞)
RELATED INFORMATIONS
- 1. If the domain of definition of function f (x) is r, for any real number a B, f (a + b) = f (a) * f (b), Let f (1) = k find f (10)
- 2. If f (lgx) > F (1), then the value range of real number x is () A. (110,1)B. (0,110)∪(1,+∞)C. (110,10)D. (0,1)∪(10,+∞)
- 3. Given the function f (x) = 2ax-x3, a > 0, if f (x) is an increasing function on X ∈ (0,1], find the value range of A
- 4. Given the function f (x) = LNX, G (x) = 1 / 2aX & # 178; + 2x, a ≠ 0. (1) if the function H (x) = f (x) - G (x) has monotone decreasing interval, find the value range of a; (2) if the function H (x) = f (x) - G (x) [1,4], find the value range of A Find the monotone interval of y = x √ (ax-x & # 178;) (a > 0)
- 5. Some derivative problems of mathematical function in Senior Two (1) The monotone interval of y = 1 / (x + 1) is determined by derivative (2) F (x) = (x ^ 2-3 / 2x) e ^ x increasing function interval
- 6. It is known that f (x) is an odd function defined on (- ∞, + ∞), and f (x) is a decreasing function on [0, + ∞) A. f(5)>f(-5)B. f(4)>f(3)C. f(-2)>f(2)D. f(-8)=f(8)
- 7. Seeking monotonicity of function Judge the monotonicity of function f (x) = x + 4 / X (x > 0) Please write down the process, and are given
- 8. When m is the value, the domain of F (x) = (MX ^ 2 + 4x + m + 2) ^ 1 / 2 + (x ^ 2-mx + 1) ^ 0 is r
- 9. When m is the value, the domain of F (x) = (MX ^ 2 + 4x + m + 2) ^ - 3 / 4 + (x ^ 2-mx + 1) is r
- 10. If the definition field of function f (x) = (MX ^ 2 + 4x + m + 2) ^ - 3 / 4 + (x ^ 2-mx + 1) ^ 1 / 2 is r, find the value range of real number M The answer is (√ 5) - 1
- 11. Given that the function FX of the domain of definition in R decreases monotonically in the interval (from negative infinity to 5), for any real number T, f (5 + T) = f (5-T) f-1
- 12. We know that the function f (x) whose domain is r decreases monotonically on (- ∞, 5). For any real number T, f (5 + T) = f (5-T), then f (- 1), f (9), f (- 13) are of the same size
- 13. It is known that the function f (x) whose domain is r decreases monotonically in the interval (- ∞, 5). For any real number T, f (5 + T) = f (5-T), then the following formula must be true () A. f(-1)<f(9)<f(13)B. f(13)<f(9)<f(-1)C. f(9)<f(-1)<f(13)D. f(13)<f(-1)<f(9)
- 14. It is known that the function f (x) whose domain is r decreases monotonically in the interval (- ∞, 5). For any real number T, f (5 + T) = f (5-T), then the following formula must be true () A. f(-1)<f(9)<f(13)B. f(13)<f(9)<f(-1)C. f(9)<f(-1)<f(13)D. f(13)<f(-1)<f(9)
- 15. The range of function f (x) = (sinx-2) / (SiNx + 1) is
- 16. Function f (x) is defined as R, satisfying f (x) = f (14-x), equation f (x) = 0 has n real roots, the sum of these n roots is 2009, then n is to process, fast
- 17. Given the function f (x) = (x ^ 2-3x-2) g (x) + 3x-4, where g (x) is a function whose domain is r, it is proved that the equation f (x) = 0 must have real roots in (1,2)
- 18. If the function f (x) satisfies f (x + 3) = f (- x + 5) in its domain of definition, and the equation f (x) = 0 has five unequal real roots, find these five roots Find the sum of the five real roots
- 19. It is known that M is a set of all functions f (x) satisfying the following properties. For function f (x), Let f (x) be a set of any two self-sufficient functions in the domain of F (x) It is known that M is a set of all functions f (x) satisfying the following properties (x) For any two independent variables X 1.x 2 in the domain, | f (x 1) - f (x 2) | ≤| x 1-x 2 | holds 1. Given that the function g (x) = ax ^ 2 + BX + C belongs to m, write the conditions that real numbers a, B, C must satisfy 2. For the element H (x) = √ (x + 1) of set M, X ≥ 0, find the minimum value of constant K satisfying the condition
- 20. It is known that a set M is a set of all functions f (x) which satisfy the following properties: for function f (x), any two different independent variables X1 and X2 in the domain of definition have | f (x1) - f (x2) | ≤| x1-x2 | (1) judge whether the function f (x) = 3x + 1 belongs to set M? (2) if G (x) = a (x + 1 x) belongs to m on (1, + ∞), find the value range of real number a