函数f(x)=(ax+1)/(x+2)在区间(-2,+∞)上单调递增,则实数a的取值范围是( )f(x)=(ax+1)/(x+2)=a-(2a-1)/(x+

函数f(x)=(ax+1)/(x+2)在区间(-2,+∞)上单调递增,则实数a的取值范围是(   )f(x)=(ax+1)/(x+2)=a-(2a-1)/(x+
f(x)=(ax+1)/(x+2)
=a-(2a-1)/(x+2)
要使y=-(2a-1)/(x+2)在(-2,+∞)上单调递增,由于-1/(x+2)在(-2,+∞)上单调递增,所以
只需令2a-1>0 即a>1/2
所以a得取值范围为(1/2,+∞)
(ax+1)/(x+2)=a+(-2a+1)/(x+2)
因为(-2,+无穷)递增,
所以-2a+1<0;
a>1/2;

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