Question

求下列函数的反函数（需要详细过程）？

Answer 1

-3π/4≤x≤π/4
-5π/12≤x+π/3≤7π/12
x≤π/6时,x+π/3=arcsin(y/5)
x>π/6时,
y=5sin(x+π/3) =5sin(2π/3-x)
2π/3-x=arcsin(y/5)
所以,反函数是：
y≤π/6时,y=arcsin(x/5)-π/3
y>π/6时,y=2π/3-arcsin(y/5)
2)
y=1/2arctan(x/3)
2y=arctanx/3
tan2y=x/3
x=3tan2y
即：反函数为：y=3tan2x,2,求下列函数的反函数（需要详细过程）
（1）y=5sin(x+π/3) （-3π/4≤x≤π/4）
（2）y=1/2arctan(x/3)