MathematicsMedium110×since 2002Q3828Let f:R→Rf:R \to Rf:R→R and g:R→Rg:R \to Rg:R→R be two functions defined by f(x)=loge(x2+1)−e−x+1f(x) = {\log _e}({x^2} + 1) - {e^{ - x}} + 1f(x)=loge(x2+1)−e−x+1 and g(x)=1−2e2xexg(x) = {{1 - 2{e^{2x}}} \over {{e^x}}}g(x)=ex1−2e2x. Then, for which of the following range of α\alphaα, the inequality f(g((α−1)23))>f(g(α−53))f\left( {g\left( {{{{{(\alpha - 1)}^2}} \over 3}} \right)} \right) > f\left( {g\left( {\alpha -{5 \over 3}} \right)} \right)f(g(3(α−1)2))>f(g(α−35)) holds ?A(2, 3)B(−-−2, −-−1)C(1, 2)D(−-−1, 1)Check answerSkip