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∃x∈R,x2﹣x﹣1≥0 ∀x∈R,x2﹣x﹣1<0 ∀x∈R,x2﹣x﹣1>0 ∀x∈R,x2﹣x﹣1≥0
f(x1)<0,f(x2)<0 f(x1)<0,f(x2)>0 f(x1)>0,f(x2)<0 f(x1)>0,f(x2)>0
∀x∈R,x2+x﹣1<0 ∀x∈R,x2+x﹣1≤0 ∃x∉R,x2+x﹣1=0 ∃x∈R,x2+x﹣1≤0
={x|﹣1<x<2}, ={x|x2+2x≤0},则A.∩B.=( ) A.{x|0<x<2}B.{x|0≤x<2} {x|﹣1<x<0} {x|﹣1<x≤0}
(2x-2)(3x-4)=0,∴2-2x=0或3x-4=0 (x+3)(x-1)=1,∴x+3=0或x-1=1 (x-2)(x-3)=2×3,∴x-2=2或x-3=3 x(x+2)=0,∴x+2=0
f(x1)<0,f(x2)<0 f(x1)<0,f(x2)>0 f(x1)>0,f(x2)<0 f(x1)>0,f(x2)>0
f(x1)<0,f(x2)<0 f(x1)<0,f(x2)>0 f(x1)>0,f(x2)<0 f(x1)>0,f(x2)>0
f(x1)<0,f(x2)<0 f(x1)<0,f(x2)>0 f(x1)>0,f(x2)<0 f(x1)>0,f(x2)>0
∀x∈R,x3﹣x2+1≤0 ∃x0∈R,x3﹣x2+1<0 ∃x0∈R,x3﹣x2+1≤0 不存在x∈R,x3﹣x2+1>0
{x│0≤x<1} {x│0≤x<2} {x│0≤x≤1} {x│0≤x≤2}
∀x∈R,2x2+1≤0 ∃x0∈R,2x02+1>0 ∃x0∈R,2x02+1<0 ∃x0∈R,2x02+1≤0
X1>X2>X0 X1=X2>X0 X1=X2<X0 X2>1>X0
对任意实数x,都有x2﹣2x+1<0 对任意实数x,都有x2﹣2x+1≤0 存在实数x,有x2﹣2x+1<0 存在实数x,有x2﹣2x+1≤0
{x|0<x≤1} {x|1<x<2} {x|0<x<1} {x|1≤x<2}
∀x>1,x2﹣2x﹣3=0 ∀x>1,x2﹣2x﹣3≠0 ∃x0≤1,x02﹣2x0﹣3=0 ∃x0≤1,x02﹣2x0﹣3≠0
f(x1)<0,f(x2)<0 f(x1)<0,f(x2)>0 f(x1)>0,f(x2)<0 f(x1)>0,f(x2)>0
f(x1)<0,f(x2)>0 f(x1)<0,f(x2)<0 f(x1)>0,f(x2)<0 f(x1)>0,f(x2)>0
If x<0 Then y=0 If x<1 Then y=1 If x<2 Then y=2 If x>=2 Then y=3 If x>=2 Then y=3 If x>1 Then y=2 If x>=0Then y=1 If x>0 Then y=0 If x<0 Then y=0 Else If>=0Then y=1 Else y=3 End If If x>=2 Then y=3 Else If>=1 Then y=2 Else y=0 End If