求f(x)=-2x^2+4x-3 ①x∈[a,2] ②[-2,-1] ③[1/2,2]的值域
问题描述：
求f(x)=-2x^2+4x-3 ①x∈[a,2] ②[-2,-1] ③[1/2,2]的值域
答
f(x) = -2x² + 4x - 3 = -2(x - 1)² - 1
①x∈[a ,2]
a 0 ≤ a ≤1 ：-3 ≤ f(x) ≤ -1
a > 1 ：-3 ≤ f(x) ≤ -2a² + 2a - 3
②x∈[-2,-1]
-19 ≤ f(x) ≤ -9
③x∈[1/2 ,2]
-3 ≤ f(x) ≤ -1