解:∵函數(shù)y=f(x)圖像的兩相鄰對稱軸的距離為π/2 ∴f(x)的周期為π 即:w=2 化簡得:f(x)=√3 sin( wx+φ)-cos(wx+φ)=2sin(2x+φ+π/6) 又∵f(x)為偶函數(shù),所以φ+π/6=π,解得φ=5π/6 所以函數(shù)f(x)=2sin(2x+π)=2cos2x(1)f(π/8)=2cos(2×π/8)=√2 (2)y=f(x)的圖像向右平移π/6 個單位,f(x)=2cos(2(x-π/6)=2cos(2x-π/3) 得到的圖像上各點的橫坐標伸長到原來的4倍g(x)=2cos(x/2-π/3)2kπ≤x/2-π/3≤2kπ+π 解得:4kπ+2π/3≤x≤4kπ+8π/3 所以,g(x)的單調遞減區(qū)間[4kπ+2π/3,4kπ+8π/3]