已知偶函数f(x)在(0,+∞)上为增函数,且f(2)=0,解不等式f[log2(x2+5x+4)]≥0.
问题描述:
已知偶函数f(x)在(0,+∞)上为增函数,且f(2)=0,解不等式f[log2(x2+5x+4)]≥0.
答
∵不等式f[log2(x2+5x+4)]≥0.且f(2)=0,∴f(log2(x2+5x+4))≥f(2).∵偶函数f(x)在(0,+∞)上为增函数,∴|log2(x2+5x+4)|≥2,∴log2(x2+5x+4)≥2或log2(x2+5x+4)≤−2.∴x2+5x+4≥22或0<x2+5x+4≤2-2,...