Problem:
Let f be the function defined by f(x)=ax2β2β for some positive a. If f(f(2β))=β2β then a=
Answer Choices:
A. 22β2ββ
B. 21β
C. 2β2β
D. 22ββ
E. 22+2ββ
Solution:
Since aξ =0, the only x for which f(x)=β2β is x=0. Since f(f(2β))=β2β,f(2β) must be 0. Thus 2aβ2β=0, or a=22ββ.
OR
Since f(2β)=2aβ2β,f(f(2β))=a(2aβ2β)2β2β which we set equal to β2β. Therefore, a(2aβ2β)2=0. Since a>0,2a=2β and a=22ββ.