Question

求问大学高数题（请写出详细步骤）

第9题的步骤应该怎么写？

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Answer 1

分段函数，将内层函数的值域看作外层函数的定义域，如下详解望采纳

追问

麻烦再写一下第11题，谢谢

追答

是2，3小问么

就是将反函数转为正弦，正切函数

Answer 2

f(x)
=1 ; x>0
=0 ; x=0
=-1 ; x<0
g(x) =2x+1
To find : f[g(x)] , g[f(x)]
solution:
2x+1 >0
x > -1/2
ie
f[g(x)]
= 1 ; x>-1/2

= 0 ; x=-1/2
=-1 ; x< -1/2
//
x>0 : g[f(x)] = g(1) = 2(1)+1 = 3
x=0 : g[f(x)] = g(0) = 2(0)+1 = 1
x<0 : g[f(x)] = g(-1) = 2(-1)+1 = -1
ie
g[f(x)]
=3 ; x>0
=1 ; x=0
=-1 ; x<0

追问

麻烦再写一下第11题

追答

11
(2)
f(x) =arcsin(x/2)
f(-2) = arcsin(-2/2)= arcsin(-1) =-π/2
f(-√3) = arcsin(-√3/2)= arcsin(-1) =-π/3
f(0) = arcsin(0/2)= arcsin(0) =0
f(1) = arcsin(1/2)= arcsin(1/2) =π/6
f(2) = arcsin(2/2)= arcsin(1) =π/2
(3)
f(x)=arctanx
f(0)=arctan(0) =0
f(1)=arctan(1) =π/4
f(√3/3)=arctan(√3/3) =π/6
f(√3)=arctan(√3) =π/3