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AoPS Wiki talk:Problem of the Day/June 5, 2011

Revision as of 20:41, 4 June 2011 by ProblemSolver747 (talk | contribs) (→‎Solution)

Problem

AoPSWiki:Problem of the Day/June 5, 2011

Solution

This Problem of the Day needs a solution. If you have a solution for it, please help us out by adding it.

First, let's simply the expression $f(x) =\frac{x}{2}-\frac{5}{2}$. We have $f(g(7+-3)+3) = f(g(4)+3).$ We know that $g(x)=4x-6$.

That implies that $g(4)=4(4)-6=10$. Now we know that $f(g(7+-3)+3) = f(10+3) = f(13) = \frac{13}{2} - \frac{5}{2} = \boxed{4}$.

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