Problem: If f(x)=log(1−x1+x) for −1<x<1, then f(1+3x23x+x3) in terms of f(x) is
Answer Choices:
A. −f(x)
B. 2f(x)
C. 3f(x)
D. [f(x)]2
E. [f(x)]3−f(x)
Solution:
f(1+3x23x+x3)=log1−1+3x23x+x31+1+3x23x+x3=log1+3x2−3x−x31+3x2+3x+x3=log(1−x)3(1+x)3=log(1−x1+x)3=3log1−x1+x=3f(x)