Question

已知函数f(x)=2sin(2x一4分之13派）…求函数的单调区间…若x属于[0,4分之3派]求f(

Answer 1

f(x)＝2sin(2x－13π/4)＝2sin(2x－13π/4＋4π)＝2sin(2x＋3π/4)

∴当2kπ－π/2≤2x＋3π/4≤2kπ＋π/2 即 kπ－5π/8≤x≤kπ－π/8时,函数f(x)单调递增

当2kπ＋π/2≤2x＋3π/4≤2kπ＋3π/2 即 kπ－π/8≤x≤kπ＋3π/8时,函数f(x)单调递减

∵x∈[0,3π/4] ∴2x∈[0,3π/2] ∴2x＋3π/4∈[3π/4,9π/4]

∴f(x)∈[﹣1,√2/2]