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− | == Problem ==
| + | #redirect [[2006 AMC 12A Problems/Problem 2]] |
− | Define <math>x\otimes y=x^3-y</math>. What is <math>h\otimes (h\otimes h)</math>?
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− | <math> \mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3 </math>
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− | == Solution ==
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− | Plugging our values into the defined [[operation]], we have
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− | <center><math>\displaystyle h\otimes h = h^3-h</math></center>
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− | Plugging in the [[function]] once more, we have
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− | <center><math>\displaystyle h\otimes(h\otimes h) = h\otimes (h^3 - h) = h^3-(h^3-h)=h</math></center>
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− | which is choice <math>(C)</math>.
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− | == See Also ==
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− | *[[2006 AMC 10A Problems]]
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