document.write( "Question 1151905: For the real-valued functions = g(x)=x^2-3 and h(x) = sqrt(x-6), find the
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Algebra.Com's Answer #773776 by Edwin McCravy(20060) $\"\"$ $\"About$

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For the real-valued functions = g(x)=x^2-3 and h(x) = sqrt(x-6), find the
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document.write( "Substitute the right side of h(x) for x in the equation for g(x)\r\n" );
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document.write( "Since g∘h = g(h(x)), we cannot substitute anything for x unless it is in the\r\n" );
document.write( "domain of h, and also what we substitute for x must not cause h(x) to produce\r\n" );
document.write( "any values which are not in the domain of g.\r\n" );
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document.write( "We find the domain of h:\r\n" );
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document.write( "-3 -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
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document.write( "which in interval notation is\r\n" );
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document.write( "The domain of g, since g is a polynomial function, is \"all real numbers\",\r\n" );
document.write( "which is written\r\n" );
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document.write( "Thus h cannot produce any value which is not in the domain of g, so the\r\n" );
document.write( "domain of g∘h is the same as the domain of h\r\n" );
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document.write( "Edwin

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