Question

证明y=x[1/(3^x-1)+1/2]在定义域上恒大于0

Answer 1

x∈(-∞,0)∪(0,+∞)

y=[x(3^x+1)]/[2(3^x-1)]

因为3^x+1＞0,

当x∈(-∞,0)时,x＜0,[2(3^x-1)]＜0,∴y＞0

当x∈(0,+∞)时,x＞0,[2(3^x-1)]＞0,∴y＞0

综上y在定义域上恒＞0