(2013•资阳一模)函数f(x)=sin2x+23cos2x−3,函数g(x)=mcos(2x−π6)−2m+3&nb
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(2013•资阳一模)函数f(x)=sin2x+2
cos
3 |
f(x)=sin2x+2
3cos2x−
3=2sin(2x+
π
3)
∵x1∈[0,
π
4]
∴2x1+
π
3∈[
π
3,
5π
6]
∴f(x1)∈[1,2]
∵x2∈[0,
π
4]
∴2x2−
π
6∈[−
π
6,
π
3]
∴cos(2x2−
π
6)∈[
1
2,1]
∵m>0
∴g(x2)=mcos(2x2−
π
6)−2m+3 (m>0)∈[−
3
2m+3,−m+3]
∵存在x1, x2∈[0,
π
4],使得f(x1)=g(x2)成立
∴
−
3
2m+3≤2
−m+3≥1
∴
2
3≤m≤2
故选C.
3cos2x−
3=2sin(2x+
π
3)
∵x1∈[0,
π
4]
∴2x1+
π
3∈[
π
3,
5π
6]
∴f(x1)∈[1,2]
∵x2∈[0,
π
4]
∴2x2−
π
6∈[−
π
6,
π
3]
∴cos(2x2−
π
6)∈[
1
2,1]
∵m>0
∴g(x2)=mcos(2x2−
π
6)−2m+3 (m>0)∈[−
3
2m+3,−m+3]
∵存在x1, x2∈[0,
π
4],使得f(x1)=g(x2)成立
∴
−
3
2m+3≤2
−m+3≥1
∴
2
3≤m≤2
故选C.
(2013•资阳一模)函数f(x)=sin2x+23cos2x−3,函数g(x)=mcos(2x−π6)−2m+3&nb
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