Question

函数~~~应该是复合函数里的设f(x)=sinx,g(x)=arccosx,写出y=f[g(x)]及y=g[f(x)]的

Answer 1

y＝f[g(x)]＝sin(arccosx)＝√(1-x^2)

y＝g[f(x)]＝arccos(sinx)＝arccos[cos(π/2－x)]

＝π/2－x,若－π/2≤x≤π/2

＝kπ＋π/2－x,若kπ－π/2≤x≤kπ＋π/2,k∈Z