Given the function f (x) = 2Sin (Wx + π / 6), w ∈ R, and w ≠ 0.1, if the image of F (x) passes through the point (π / 6,2) and 0 < w < 3, find the value of W. 2. Under the condition of the first question, sun function g (x) = MF (x) + n (m > 0), when x ∈ [0, π / 2], what is the range of G (x)

Given the function f (x) = 2Sin (Wx + π / 6), w ∈ R, and w ≠ 0.1, if the image of F (x) passes through the point (π / 6,2) and 0 < w < 3, find the value of W. 2. Under the condition of the first question, sun function g (x) = MF (x) + n (m > 0), when x ∈ [0, π / 2], what is the range of G (x)

Solution: (1) substituting the point (π / 6,2) into the original number: F (x) = 2Sin (Wx + π / 6), we can get: 2 = 2Sin (w π / 6 + π / 6), sin90 = 1, and 0