2006 AMC 10A Problems/Problem 2

Revision as of 09:14, 28 July 2006 by JBL (talk | contribs) (Solution)

Problem

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 into the defined operation, we have

$\displaystyle h\otimes h = h^3-h$

Plugging in the function once more, we have

$\displaystyle h\otimes(h\otimes h) = h\otimes (h^3 - h) = h^3-(h^3-h)=h$

which is choice $(C)$.

See Also

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