Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 5, 2011"

Latest revision as of 21:52, 4 June 2011

First, let's simply the expression $f(g(7+-3)+3)$ . 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 $f(g(7+-3)+3) = f(g(4)+3) = f(10+3) = f(13) = \frac{13}{2} - \frac{5}{2} = \boxed{4}$ .

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 {{:AoPSWiki:Problem of the Day/June 5, 2011}}
 ==Solution==
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 First, let's simply the expression <math> f(g(7+-3)+3) </math>.  We have <math>f(g(7+-3)+3) = f(g(4)+3).</math>  We know that <math>g(x)=4x-6</math>.
 That implies that <math>g(4)=4(4)-6=10</math>.  Now we know that <math>f(g(7+-3)+3) =  f(g(4)+3) = f(10+3) = f(13) = \frac{13}{2} - \frac{5}{2} = \boxed{4}</math>.