2006 AMC 12A Problems/Problem 4

Define $x\otimes y=x^3-y$ . What is $h\otimes (h\otimes h)$

$\mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3$

Solution

Plugging our values in the function, we have

$\displaystyle h^3-h$

Plugging in the function once more, we have

$\displaystyle h^3-(h^3-h)=h, (C)$