Problem: Let F=log1βx1+xβ. Replace each x in F by 1+3x23x+x3β, and simplify. The simplified expression is equal to:
Answer Choices:
A. βF
B. F
C. 3 F
D. F3
E. F3βF
Solution:
Since 1β1+3x23x+x3β1+1+3x23x+x3ββ=1β3x+3x2βx31+3x+3x2+x3β=(1βx)3(1+x)3β=(1βx1+xβ)3, we have
F(new)=log(1βx1+xβ)3=3log1βx1+xβ=3F(original)