已知f(x)=32x-(k+1)3x+2,当x∈R时,f(x)恒为正值,则k的取值范围是( ) A.(-∞,-1) B.(-∞,22-1) C.(-1,22-1) D.(-22-1,22-1)
问题描述:
已知f(x)=32x-(k+1)3x+2,当x∈R时,f(x)恒为正值,则k的取值范围是( )
A. (-∞,-1)
B. (-∞,2
-1)
2
C. (-1,2
-1)
2
D. (-2
-1,2
2
-1)
2
答
令3x=t (t>0),则g(t)=t2-(k+1)t+2,若x∈R时,f(x)恒为正值,则g(t)=t2-(k+1)t+2>0对t>0恒成立.∴k+12>0(k+1)2−8<0 ①或k+12≤0g(0)=2>0 ②解①得:-1<k<-1+2...