Given f (x) = 2 + log3x (1 ≤ x ≤ 9), the maximum and minimum values of the function g (x) = [f (x)] 2 + F (x2) are obtained

Given f (x) = 2 + log3x (1 ≤ x ≤ 9), the maximum and minimum values of the function g (x) = [f (x)] 2 + F (x2) are obtained

From the definition field of F (x) as [1,9], we can get that the definition field of G (x) is [1,3], and G (x) = (2 + log3x) 2 + (2 + log3x2) = (log3x + 3) 2-3, ∵ 1 ≤ x ≤ 3, ∵ 0 ≤ log3x ≤ 1. When x = 1, G (x) has a minimum value of 6; when x = 3, G (x) has a maximum value of 13

Simple logarithmic function in Senior High School
Let the second third power of log with a as the base be less than 1, then the value range of A
I don't understand why the final answer is from 1 to infinity. Thank you first

I think you'd better read his formula in the book first
loga,2/3

Given function f (x) = log4 (AX & # 178; + 2x + 3)
If there is a real number a, the minimum value of F (x) is 1. If there is, the value of a can be obtained. If not, please explain the reason

To make f (x) minimum 1, the minimum value of G (x) = ax ^ 2 + 2x + 3 must be 4
When a = 0, G (x) = 2x + 3 has no minimum value
When a is not 0,
g(x)=a(x+1/a)^2+3-1/a
Only when a > 0, the minimum value = 3 - 1 / a = 4, a = - 1, contradiction
So there is no such a value