2006 AMC 10A Problems/Problem 2
Problem
Define . What is
?
Solution
Plugging our values into the defined operation, we have
![$\displaystyle h\otimes h = h^3-h$](http://latex.artofproblemsolving.com/8/8/9/8892c3bc6b62232b00e7e1b29d130a6604e81d5f.png)
Plugging in the function once more, we have
![$\displaystyle h\otimes(h\otimes h) = h\otimes (h^3 - h) = h^3-(h^3-h)=h$](http://latex.artofproblemsolving.com/6/5/5/6559ff3d11843679e8140586d4a33e08aa3ce5c0.png)
which is choice .
See also
2006 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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All AMC 10 Problems and Solutions |