document.write( "Question 1194123: given the functions f(x)=x+2 and g(x)=x^2, determine all values of x for which f(g(x))=g(f(x)). \n" ); document.write( "

Algebra.Com's Answer #826235 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "given the functions f(x)=x+2 and g(x)=x^2, determine all values of x for which f(g(x))=g(f(x)).
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document.write( "Left side of this equation is\r\n" );
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document.write( "    f(g(x)) = g(x) + 2 = x^2 + 2.\r\n" );
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document.write( "Right side of this equation is\r\n" );
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document.write( "    g(f(x)) = (f(x))^2 = (x+2)^2 = x^2 + 4x + 4.\r\n" );
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document.write( "So, this equation  f(g(x))=g(f(x))  takes the form\r\n" );
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document.write( "    x^2 + 2 = x^2 + 4x + 4.\r\n" );
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document.write( "Cancel the terms x^2 in both sides; keep the term with x in right side; collect constant terms in left side\r\n" );
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document.write( "    2 - 4 = 4x\r\n" );
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document.write( "      -2  = 4x\r\n" );
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document.write( "      -1/2  =  x.\r\n" );
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document.write( "ANSWER.  x = -1/2.\r\n" );
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