y=log2(-x²+2x)求函数值域

y=log2(-x²+2x)求函数值域
y=log2(-x²+2x)求函数值域

y=log2(-x²+2x)求函数值域
y=log2(-x²+2x)
=log2[-(x-1)²+1]
因为 -(x-1)²+1≤1
所以
y=log2[-(x-1)²+1]≤0
则值域为 (负无穷,0]

(负无穷，log2)

f(x) = -x² + 2x = -(x² - 2x + 1 - 1) = -(x - 1)² + 1，f(x)max = f(1) = 1
ymax = 0
ymin ＞-∞
y∈(-∞，0]