求f(x)=-2x^2+4x-3 ①x∈[a,2] ②[-2,-1] ③[1/2,2]的值域

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求f(x)=-2x^2+4x-3 ①x∈[a,2] ②[-2,-1] ③[1/2,2]的值域
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求f(x)=-2x^2+4x-3 ①x∈[a,2] ②[-2,-1] ③[1/2,2]的值域
求f(x)=-2x^2+4x-3 ①x∈[a,2] ②[-2,-1] ③[1/2,2]的值域

求f(x)=-2x^2+4x-3 ①x∈[a,2] ②[-2,-1] ③[1/2,2]的值域
f(x) = -2x² + 4x - 3 = -2(x - 1)² - 1
①x∈[a ,2]
a < 0 :-2a² + 2a - 3 ≤ f(x) ≤ -1
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