University of South Carolina High School Math Contest/1993 Exam/Problem 2
Problem
Suppose the operation is defined by
If
then
![$\mathrm{(A) \ } 2 \qquad \mathrm{(B) \ }3\qquad \mathrm{(C) \ }4 \qquad \mathrm{(D) \ }5 \qquad \mathrm{(E) \ }6$](http://latex.artofproblemsolving.com/7/f/c/7fca7225123463e8169320ea40b76b9cb84e5c09.png)
Solution
, so the answer is
.
Alternatively, note the resemblence to Simon's Favorite Factoring Trick. so
so
and
.