已知f(x)=2sin(2/3πx+π/6).若函数f(x)满足方程f(x)=a (12/3πx=2πx/3

已知f(x)=2sin(2/3πx+π/6).若函数f(x)满足方程f(x)=a (12/3πx=2πx/3
已知f(x)=2sin(2/3πx+π/6).若函数f(x)满足方程f(x)=a (1
2/3πx=2πx/3

已知f(x)=2sin(2/3πx+π/6).若函数f(x)满足方程f(x)=a (12/3πx=2πx/3
f(x)=2sin(2/3πx+π/6).容易求对称轴 即2πx/3+π/6=π/2+2kπ
f(x)=a(1

2sin(2πx/3+π/6)=a
sin(2πx/3+π/6)=a/2
2πx/3+π/6+2kπ=arcsin(a/2)
arcsin(a/2)=2πx/3+π/6+2kπ
x=-1/4-3k+(3/2π)arcsin(a/2)
1＜a＜2
1/2＜a/2＜1
π/6＜arcsin(a/2)＜π-π/6=5π/6,arcsin(a/2)≠...

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2sin(2πx/3+π/6)=a
sin(2πx/3+π/6)=a/2
2πx/3+π/6+2kπ=arcsin(a/2)
arcsin(a/2)=2πx/3+π/6+2kπ
x=-1/4-3k+(3/2π)arcsin(a/2)
1＜a＜2
1/2＜a/2＜1
π/6＜arcsin(a/2)＜π-π/6=5π/6,arcsin(a/2)≠2kπ+π/2
π/6＜2πx/3+π/6+2kπ＜5π/6,arcsin(a/2)≠2kπ+π/2
-2k＜2x/3＜-2k+2/3,2πx/3+π/6+2kπ≠2kπ+π/2
-3k＜x＜-3k+1,x≠1/2
0≤x≤9
-3k＜0≤x≤9＜-3k+1
k=0,0＜x＜1/2,1/2＜x＜1,x1=-1/4+(3/2π)arcsin(a/2)
k=-1,3＜x＜7/2,7/2＜x＜4,x2=-1/4+3+(3/2π)arcsin(a/2)
k=-2,6＜x＜13/2,13/2＜x＜7,x3=-1/4+6+(3/2π)arcsin(a/2)
x1+x2+x3=9-3/4+(9/2π)arcsin(a/2)

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