The function f (x) is an even function on R, and is a decreasing function on (- 00,0). Compare the size of F (- 7 / 8) and f (2a ^ 2-A + 1)

The function f (x) is an even function on R, and is a decreasing function on (- 00,0). Compare the size of F (- 7 / 8) and f (2a ^ 2-A + 1)

Compare! - 7 / 8! With! (2a ^ 2-A + 1)! In size
(2a ^ 2-A + 1) > 0 a = 1 / 4 minimum 7 / 8
(2a^2-a+1)≥7/8
So f (- 7 / 8) ≤ f (2a ^ 2-A + 1)

It is known that y = f (x) is an even function and an increasing function on (- infinity, 0). Try to compare the magnitude of F (- 7 / 8) and f (1)

Because f (x) is an even function,
So, f (x) = f (- x)
So, f (1) = f (- 1)
And because the function increases from negative infinity to zero,
Therefore, f (- 7 / 8) > F (- 1)
Therefore, f (- 7 / 8) > F (1)

The function y = f (x) is an even function, and it is an increasing function in (- ∞, 0]. Compare the size of F (- 8 / 7) and f (1)

f(1)=f(-1)
Because in (- ∞, 0], the increasing function
So f (- 1) > F (- 8 / 7)

If 1 is less than or equal to X and less than or equal to 100, find the maximum value of function f (x) = LG (x / a) * LG (a ^ 3 * x)

F (x) = LG (x / a) * LG (a ^ 3 * x) = (lgx LGA) * (3lga + lgx) = (lgx + LGA) & # 178; - 4 (LGA) & # 178; ∵ 1 less than or equal to x less than or equal to 100 ∵ 0 ≤ lgx ≤ 2 (1) when 0 ≤ a ＜ 1 / 100, f (x) = LG (x / a) * LG (a ^ 3 * x) has the minimum value (2 + LGA) & # 178; - 4 (LGA) & # 178; = 2 + 4lga-3 (LGA) & # 1