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

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• 1. 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),
• 2. Monotone decreasing interval of function f (x) = sin (x + Pai / 6) + sin (x-pai / 6) + cosx minimum positive period sum on [0,2pai]
• 3. The known function f (x) = 2asinx * cosx + 2cos ^ 2x + 1, f (π / 6) = 4 Find the real number a Finding the symmetric center coordinates of the function f (x) image Finding the range of function f (x) on [- π / 4, π / 4]
• 4. The piecewise function f (x) = {x2-x + 1 (x > = 2) x + 1 (x) is known
• 5. Draw the program block diagram of the function f (x) = x + 1
• 6. Let the maximum value of the function y = x ^ 3-2x + A in the interval [1,2] be 8, then what is the value of a
• 7. The quadratic function y = - x squared - 4x-5 is known (1) Translate the image of the quadratic function up and down so that its vertex just falls on the image of the positive scale function y = - x, and find the analytic expression of the quadratic function at this time
• 8. The quadratic function y = 2x ^ - 8x + 3 is transformed into y = a (x + H) ^ 2 + K by collocation method
• 9. (1) the quadratic function y = x2-4x + 3 is changed into the form of y = (X-H) 2 + K by the collocation method;
• 10. Given the function f (x) = x ^ 2-2x + 2, y = f (x), the minimum value on [T, t + 1] is the function g (x) of T, the analytic expression of G (x) is obtained
• 11. 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
• 12. 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}
• 13. 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)
• 14. If the domain of F (X & # 178;) is [- 1,1], the domain of F (x) is
• 15. 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
• 16. 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
• 17. 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
• 18. 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)
• 19. 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
• 20. 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)