The range of y = 2cos (2x + π / 3) + 1, X ∈ [0, π / 2]

Let 2x + π|3 = t
Because x ∈ [0, π / 2]
So 0 "2x" π
π/3《2X+π|3《4π/3
So π / 3 T 4 π / 3
Y=2cosT (π/3《T《4π/3)
From the image of y = cosx
Y=cosT T∈【π/3,4π／3】
The value range of is [- 1, &189;]
Therefore, the value range of y = 2cost + 1 is [- 1,2]

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