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

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

Y = f (x) ^ 2 + F (x ^ 2) = (2 + log3x) ^ 2 + 2 + log3 (x ^ 2) = (log3x) ^ 2 + 6log3x + 6. In this case, 1 "X" 9, and 1 "x ^ 2" 9, then the value range of X is 1 "X" 3 (note that the range of X of function y is different from that of F (x), here is the error prone point)

Given f (x) = 2 + log3 ^ x (1 / 81 ≤ x ≤ 9), find the maximum and minimum values of the function g (x) = [f (x)] ^ 2 + F (x ^ 2)

The definition domain of G (x) is: 1 / 81 ≤ x ≤ 9 and 1 / 81=

Given the function f (x) = log3x-3 (1 ≤ x ≤ 3), Let f (x) = [f (x)] ^ 2 + F (x ^ 2) (1) find the definition field of F (x) (2) find the maximum and minimum value of F (x)

(1) From the meaning of the question, we can get: 1 ≤ x ≤ 3 and 1 ≤ x ^ 2 ≤ 3. Combined with the image, we can get x ∈ [1, √ 3]. (2) f (x) increases on [1, √ 3], (we can get f (x) ∈ [- 3, - 5 / 2]), so [f (x)] ^ 2 decreases on [1, √ 3], so f (x ^ 2) decreases on [1, √ 3], so f (x) decreases on [1, √ 3]