Find the maximum value of the interval of the function f (x) = log2 (4x) * log2 (8x), X ∈ [1 / 8,4]

F (x) = (log24 + log2x) (log28 + log2x) = (2 + log2x) (3 + log2x) = (log2x) ^ 2 + 5log2x + 6, let t = log2x, X belong to [1 / 8,4], then t belongs to [- 3,2], so g (t) = T ^ 2 + 5T + 6 = (T + 5 / 2) ^ 2 + 6-25 / 4 = (T + 5 / 2) ^ 2-1 / 4, the symmetry axis is t = - 5 / 2, so the minimum value is g (- 5 / 2) = - 1 / 4, the maximum value is

RELATED INFORMATIONS

1. The function f (x) = log2 (x + 8-b / x) is an increasing function on [1, + ∞). Find the value range of real number B
2. Let f (x) = log2 (x + a) - B, where the image of a given function passes through (- 1,0) (1,1), find the analytic expression and negative interval of real numbers a, B and the function
3. Find the x power + 1 of inverse function y = 10
4. F (x) = LG [x + √ (x ^ 2 + 1)] to find the inverse function of F (x) Each step is more detailed The answer is y = 1 / 2 (10 ^ X-10 ^ - x)
5. Y = ax + 1 / B + 2x inverse function If (1.2) is on the image of function y (B + 2x) = ax + 1 and on its inverse function image, find f (x)
6. The image of function y = ax + 1 / 3-2x can be obtained by which inverse function after proper translation Please write the process
7. If the function f (x) = a + 3 / X-B and the function g (x) 1 + C / 2x + 1 are reciprocal functions, the values of a, B and C are obtained fast
8. If the inverse function of F (x) = (2x-1) / (x + a) is itself, then the value of a is
9. Given f (x) = (2x + 1) / (x + a), [x ≠ - A, a ≠ 1 / 2], find the inverse function of F (x); if f (x) = f - &# 185; (x), find the value of A
10. When the function y = ax + B and its inverse function are the same function, the values of a and B are A.a=1,b=0 B.a=-1,b=0 C.a=±1,b=0 D. A = 1, B = 0 or a = - 1, B takes any real number
11. Finding the inverse function of F (x) = 3 ^ x
12. What is the inverse function of F (x) = 3 ^ (x + 3)
13. F (x) = 9 ^ x-3 ^ (x + 2), finding f ^ (- 1) (0) is to find the inverse function of F (x), and the value of x = 0
14. Given f (x) = x ^ 3 + X, find the inverse function of F (x)
15. If y = f (x) has an inverse function and the inverse function of y = f (x + 2) is y = f '(x-1), then the value of F' (1) - f '(0) is () What I did: from the known: F (x + 2) = X-1 Let t = x + 2, x = T-2 f(t)=t-3 f(x)=x-3 f'(x)=x+3 So f '(1) = 4, f' (0) = 3 So f '(1) - f' (0) = 1, why not? The answer is 2
16. Do y = x Λ 2 + 1, X ∈ R have inverse function?
17. F (x) R-R finding the inverse function of F (x) = y = x + 2 ^ x
18. Is the inverse function y = f (x) y = F-1 (x) y = 1 / F (x)?
19. Inverse function of y = f (x + 2) - 1 \(≧▽≦)/~
20. The inverse function of y = f (x + 1) + 1 is?)