(理)y=2arccos(x-2)的反函数是( ) A.y=12cos(x−2),(0≤x≤π) B.y=cos(x-2),(0≤x≤2π) C.y=cosx2+2,(0≤x≤2π) D.y=cos(x2+2),(0≤x≤π)
问题描述:
(理)y=2arccos(x-2)的反函数是( )
A. y=
cos(x−2),(0≤x≤π)1 2
B. y=cos(x-2),(0≤x≤2π)
C. y=cos
+2,(0≤x≤2π)x 2
D. y=cos(
+2),(0≤x≤π) x 2
答
∵y=2arccos(x-2)其中arccos(x-2)∈[0,π]
∴arccos(x-2)=
即x-2=cosy 2
y 2
∴x=cos
+2,y∈[0,2π]y 2
则f-1(x)=cos
+2,x∈[0,2π]x 2
故选C.