2006 AMC 10A Problems/Problem 2: Difference between revisions

Revision as of 14:36, 4 August 2006

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

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

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 $(C)$ .

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 == See Also ==
 *[[2006 AMC 10A Problems]]
+*[[2006 AMC 10A Problems/Problem 1|Previous Problem]]
+*[[2006 AMC 10A Problems/Problem 3|Next Problem]]
+[[Category:Introductory Algebra Problems]]