How many triangles are there if the sides of ABC are all integers and the maximum side is 4

How many triangles are there if the sides of ABC are all integers and the maximum side is 4

6

If f (x) = log2 (X & # 178; - 2aX + 3) on [0,1] is the value range of a decreasing function

From the property of the same increase different decrease of the composite function, we know that G (x) = x & # 178; - 2aX + 3 is a decreasing function on [0,1], and G (x) > 0 holds
Therefore, the symmetric axis X = a > = 1 and G (1) > 0 should be satisfied, and the solution is 1

If f (x) = log2 (X & # 178; - 2aX + 3) is a decreasing function on [0,1], the value range of a is obtained

If the outer function is an increasing function on [0,1], the inner function is required to be a decreasing function on [0,1]. If x = a is found, a > = 1 is required. At the same time, if x = 1, the inner function is required to be greater than 0, that is, a