document.write( "Question 530063: I've been trying to solve this for a few days and am having no luck and need some help please.
\n" ); document.write( "f(x)=sqrt x g(x)=x^2 and h(x)= x+2. Write q(x)=sqrt x^2+4x+4 as a composition of f, g, h. \n" ); document.write( "

Algebra.Com's Answer #349873 by Edwin McCravy(20056) $\"\"$ $\"About$

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I've been trying to solve this for a few days and am having no luck and need some help please.
\n" ); document.write( "f(x)=sqrt x g(x)=x^2 and h(x)= x+2. Write q(x)=sqrt x^2+4x+4 as a composition of f, g, h.
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document.write( "We start with\r\n" );
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document.write( "q(x) = \r\n" );
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document.write( "Since f(x) =  we can write  as f(x²+4x+4)\r\n" );
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document.write( "q(x) = f(x²+4x+4)\r\n" );
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document.write( "We factor the trinomial:\r\n" );
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document.write( "q(x) = f((x+2)(x+2))\r\n" );
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document.write( "We write that product as the square of a binomial:\r\n" );
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document.write( "q(x) = f((x+2)²)\r\n" );
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document.write( "Since g(x)=x², we can write (x+2)² as g(x+2)\r\n" );
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document.write( "q(x) = f(g(x+2))\r\n" );
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document.write( "Since h(x) = x+2, we can write g(x+2) as g(h(x))\r\n" );
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document.write( "q(x) = f(g(h(x)))\r\n" );
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document.write( "and we can write that using the composition notation as\r\n" );
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document.write( "q(x) = f∘(g∘h(x))\r\n" );
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document.write( "And maybe the parentheses can be eliminated and we can just\r\n" );
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document.write( "q(x) = f∘g∘h(x)\r\n" );
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document.write( "Edwin

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