y=(tanx)^2+3tanx+2,x∈[-π⼀4,π⼀2],则其值域为_

2025-06-26 19:17:09
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回答1:

y=(tanx)^2+3tanx+2,x∈[-π/4,π/2],则其值域为_

令tanx=a,
由于x∈[-π/4,π/2],那么a>=-1
y=(a)^2+3a+2 a>=-1

y=(a)^2+3a+2=(a+2)(a+1)

y>=0