Let f:R→R and g:R→R be two functions defined by f(x)=loge(x²+1)−e−x+1 and g(x)=1−2e2xex. Then, for which of the following range of α, the inequality f(g((α−1)23))>f(g(α−53)) holds?
A. (−2,−1)
B. (2,3)
C. (−1,1)
D. (1,2)