Problem: Let F=log1−x1+x. Replace each x in F by 1+3x23x+x3, and simplify. The simplified expression is equal to:
Answer Choices:
A. −F
B. F
C. 3 F
D. F3
E. F3−F
Solution:
Since 1−1+3x23x+x31+1+3x23x+x3=1−3x+3x2−x31+3x+3x2+x3=(1−x)3(1+x)3=(1−x1+x)3, we have
F(new)=log(1−x1+x)3=3log1−x1+x=3F(original)