Problem:
For any three real numbers a, b, and c, with bî€ =c, the operation Ψ is defined by:
Ψ(a,b,c)=b−ca​.
What is Ψ(Ψ(1,2,3),Ψ(2,3,1),Ψ(3,1,2))?
Answer Choices:
A. −21​
B. −41​
C. 0
D. 41​
E. 21​
Solution:
Because
Ψ(1,2,3)Ψ(3,1,2)​=2−31​=−1,Ψ(2,3,1)=3−12​=1, and =1−23​=−3​
we have
Ψ(Ψ(1,2,3),Ψ(2,3,1),Ψ(3,1,2))​=Ψ(−1,1,−3)=1−(−3)1​=−41​.​
Answer: B​.
The problems on this page are the property of the MAA's American Mathematics Competitions