已知f(x)=lg(x+1),g(x)=2lg(2x+t)(t∈R,t是参数).

f(x)≤g(x)lg(x+1)≤2lg(2x+t)x+1≤(2x+t)^2F(x)=4x^2+(4t-1)x+t^2-1≥0△=(4t-1)^2-4*4(t^2-1)=-8t+17≤0,t≥17/8时,F(x)≥0恒成立△>0时对称轴-(4t-1)/8≥1,t≤1/4时F(1)=4+(4t-1)+t^2-1=t^2+4t+2=(t+2)^2-2≥0t≥-2+√2,或,t≤-2-√2即:-2+√2≤t≤1/4,或,t≤-2-√2对称轴-(4t-1)/8≤0,t≥1/4时F(0)=t^2-1≥0t≥1,或,t≤-1即：t≥1所以,参数t的取值范围:(-∞,-2-√2]U[-2+√2,1/4]U[1,+∞)