題目應(yīng)該是x∈(-π/3,π/3),題都寫錯的人是極不認真的人,不認真的人怎么能學好數(shù)學,數(shù)學是嚴謹?shù)?
對于這樣的函數(shù),首先將其轉(zhuǎn)化成標準式,即y=-2sin(2x-π/3),寫出它的一個單調(diào)區(qū)間.依題意,當2x-π/3∈[2kπ-π/2 2kπ+π/2]時為減函數(shù)；2x-π/3∈[2kπ+π/2 2kπ+3π/2] 時為增函數(shù).
當x∈[kπ-π/12 kπ+5π/12],對k進行嘗試取值,使之落到(-π/3,π/3)的范圍,得出x∈[-π/12 π/3)為減函數(shù).
當x∈[kπ+5π/12 kπ+11π/12],對k進行嘗試取值,使之落到(-π/3,π/3)的范圍,得出x∈（-π/3 -π/12]時為增函數(shù).
因此,函數(shù)的單調(diào)減區(qū)間為[-π/12 π/3),單調(diào)增區(qū)間為（-π/3 -π/12].
將x=-π/12、-π/3、 π/3時的值分別為2,0,-2sinπ/3,故函數(shù)的值域為（-根3 2].