It is known that the function f (x) whose domain is R is an even function. When x ≥ 0, f (x) = (x + 1) divided by X, it is proved that f (x) = 2 ^ (1-x) has a solution in the interval (1,2)

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1. Let f (x) be an even function of the domain of definition on R, and if x > 0, f (x) = x (X-2), then find if X
2. Given the function f (x) = 2 + log3x (1 ≤ x ≤ 9), find the maximum and minimum value of the function y = [f (x) ^ 2 + F (x ^ 2), and find the corresponding value Can you add the value of F (x ^ 2) to the value of y = f (x) ^ 2
3. If the definition field of function f (X & # 178; - 1) is [- 1,2], then the value range of X in function f (√ x) is X ∈ [- 1,2] → X & # 178; - 1 ∈ [- 1,3], ■ √ x ∈ [- 1,3] → x ∈ [0,9]. I don't understand how X & # 178; - 1 ∈ [- 1,3], and then get x ∈ [0,9] It's a bit confusing. Is the analytic expression of F (X & # 178; - 1) and f (√ x) the same, with the same range, but the whole (X & # 178; - 1, √ x) as X is different, so the definition field of X in that whole is required
4. If the domain of F (X & # 178;) is [- 1,1], the domain of F (x) is
5. Let f (x) and G (x) be the even and odd functions of R respectively in the domain of definition, f (x) = 2F (x) + G (x) = MX ^ 2 + NX + 1, f (1) = 1, f (- 1) = 5, M, n Finding f (2) and G (2)
6. Let even function f (x) satisfy f (x) = 2 & # 710; x-4 (x ≥ 0), then {x| f (X-2) > 0}= 1. {x | x 〈 - 2 or X 〉 4} 2. {x | x ＜ 0 or X ＞ 4} 3. {x | x ＜ 0 or X ＞ 6} 4. {x | x ＜ - 2 or X ＞ 2}
7. Let even function f (x) satisfy f (x) = x ^ 3-8 (x > = 0), if f (X-2) > 0, then the value range of X is? Did you answer that before? I can't see it. Can you answer it again
8. Which of the following functions are odd or even? Which are not odd or even? (1) f (x) = 5x + 3 (2) f (x) = 5x (3) f (x) = x & # 178; + 1
9. Let f (x) (x ∈ R) be a periodic function with Z as the minimum positive period, and f (x) = (x-1) ^ 2 when x ∈ [0,2]. Find the values of F (3), f (7 / 2),
10. Monotone decreasing interval of function f (x) = sin (x + Pai / 6) + sin (x-pai / 6) + cosx minimum positive period sum on [0,2pai]
11. It is known that f (x) is an even function, G (x) is an odd function, and f (x) + G (x) = 1 / X-1 over the common domain {x ∈ R, X ≠ ± 1}, Find the analytic expression of F (x) The correct answer is... F (x) + G (x) = 1 / (x-1)... Sorry... Ask for the correct answer again
12. Let f (x) be defined as (- L, l). It is proved that there must exist even function g (x) and odd function H (x) on (- L, l) such that f (x) = g (x) + H (x) Suppose g (x) and H (x) exist, such that f (x) = g (x) + H (x), (1), And G (- x) = g (x), H (- x) = - H (x) So f (- x) = g (- x) + H (- x) = g (x) - H (x), (2) Using (1) and (2), G (x) = [f (x) + F (- x)] / 2 h(x)=[f(x)-f(-x)]/2 Then G (x) + H (x) = f (x), g(-x)=[f(-x)+f(x)]/2=g(x), h(-x)=[f(-x)-f(x)]/2=h(x). I can't understand the proof process of this problem. He first assumes that G (x) and H (x) exist, and satisfies f (x) = g (x) + H (x), and obtains formula (2). Then he uses the conclusions (1) and (2) obtained from the hypothesis to prove that the original hypothetical sentence is true. How can the proof be correct, The last line should be h (- x) = [f (- x) - f (x)] / 2 = - H (x)
13. Ask y = ax + B / X (Nike function) when a, B different sign of the range and image?
14. Nike function problem! Online and so on! How to find the maximum value of (X-2) + (X-2 / 2) + 4! It's a specific process The more detailed the better! It's not Nike function. How to solve it!
15. The range of function y = LG (x ^ + 1)
16. logx4＜2 , logx2＞-1, logx2＜1/3,log3x＜0,logx3＞1,log1/3x＞-1,log1/3x＞3,log1/2x＜2
17. Let f (x) = loga (1-x) g (x) = loga (1 + x)! Let f (x) = loga (1-x) g (x) = loga (1 + x), (a > 0, a ≠ 1) The number of real roots of the equation a ^ (g (x-x ^ 2 + 1)) = a (f (k)) - x about X is discussed The number of real roots of the equation a ^ (g (x-x ^ 2 + 1)) = a ^ (f (k)) - x about X is discussed
18. Is there a formula for logarithm? A ^ log a ^ n = n?
19. Can the derivative of an expression with logarithmic function be negative?
20. Logarithmic function y = loga (x) (a > 1), when x belongs to [2,4], the maximum value of the function is 1 more than the minimum value, and the value of a is obtained