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数学
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求f﹙x﹚=5-x+√3x-1的值域
人气:403 ℃ 时间:2020-06-20 14:13:29
解答
令 t=√(3x-1)
有:x=(t^2 +1)/3 (t ≥ 0)
于是:f(x)=5-(t^2 +1)/3 + t(t ≥ 0)
===> f(x)=(-t^2 +3t +14)/3 (t ≥ 0)
===> f(x)=(-t^2 +3t +14)/3 (t ≥ 0)
===> f(x)=[65/4-(t-3/2)^2 ] / 3 (t ≥ 0)
===> f(x) ≤ 65/12
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