Question

高中函数题目，急啊~~~~·

已知f(X)=4/3x+√(9-x^2),求其值域

Answer 1

换元。可设x=3cost,(0≤t≤180º.f(x)=f(t)=4cost+3sint=5sin(t+m).(m为锐角，sinm=4/5,cosm=3/5.).由m≤t+m≤180º+m.可知，-4/5≤sin(t+m)≤1===>-4≤f(x)≤5.故值域为[-4,5].