Difference between revisions of "2006 AMC 10A Problems/Problem 2"

 
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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>
 
<math> \mathrm{(A) \ } -h\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } h\qquad \mathrm{(D) \ } 2h\qquad \mathrm{(E) \ } h^3 </math>
 
== Solution ==
 
== Solution ==
 +
Plugging our values in the function, we have
 +
 +
<center><math>h^3-h</math></center>
 +
 +
Plugging in the function once more, we have
 +
 +
<center><math>h^3-(h^3-h)=h, (C)</math></center>
 
== See Also ==
 
== See Also ==
 
*[[2006 AMC 10A Problems]]
 
*[[2006 AMC 10A Problems]]

Revision as of 13:22, 3 July 2006

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 in the function, we have

$h^3-h$

Plugging in the function once more, we have

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

See Also

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