f=（ax+1）/（x+2a）(x≠-2a)
= [a(x+2a)+1-2a²]/(x+2a)
=a+(1-2a²)/(x+2a)
f(x)在區(qū)間(-2,正無(wú)窮)上是增函數(shù),
(1) -2a≤-2 ,a≥1
(2) 1-2a²1/2,
==>a√2/2
∴a的取值范圍是a≥1x=-2a是間斷點(diǎn)f(x)在區(qū)間(-2,正無(wú)窮)上是增函數(shù),間斷點(diǎn)不能在區(qū)間內(nèi)部∴-2a≤-2 f(x)的圖像是由反比例函數(shù)y=(1-2a²)/x平移而來(lái)的 反比例系數(shù)只有當(dāng)1-2a²<0時(shí) ，y=(1-2a²)/x在(0,+∞),(-∞,0)上分別是減函數(shù) ∴要1-2a²<0