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求函数y=arcsin(x-1)/4的反函数,并求其反函数的定义域和值域?
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先求函数y=arcsin(x-1)/4的定义域和值域,准备作反函数的值域和定义域
|x-1|<=1,0<=x<=2,
-π/2<=arcsin(x-1)<=π/2
-π/8<=y<=π/8
y=arcsin(x-1)/4
4y=arcsin(x-1)
sin4y=x-1
x=sin4y+1
反函数y=sin4x+1,定义域[-π/8,π/8],值域[0,2]
|x-1|<=1,0<=x<=2,
-π/2<=arcsin(x-1)<=π/2
-π/8<=y<=π/8
y=arcsin(x-1)/4
4y=arcsin(x-1)
sin4y=x-1
x=sin4y+1
反函数y=sin4x+1,定义域[-π/8,π/8],值域[0,2]
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