document.write( "Question 1048295: if f(x^2 +1)=x^4+5x^2+3. what is f(x^2 -1) \n" ); document.write( "
Algebra.Com's Answer #663923 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "if f(x^2 +1)=x^4+5x^2+3. what is f(x^2 -1)
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document.write( "My goal now is to present the polynomial in the right side,  \"x%5E4+%2B5x%5E2+%2B3\",  as a function (as a polynomial) of the argument  \"x%5E2%2B1\".  \r\n" );
document.write( "We have\r\n" );
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document.write( "\"x%5E4+%2B5x%5E2+%2B3\" = \"%28x%5E2%2B1%29%5E2\" + \"3x%5E2+%2B+2\" = \"%28x%5E2%2B1%29%5E2\" + \"3x%5E2+%2B+3\" -  \"1\" = \"%28x%5E2%2B1%29%5E2+%2B+3%2A%28x%5E2%2B1%29+-1\".\r\n" );
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document.write( "Thus  \"f%28x%5E2+%2B1%29\" = \"%28x%5E2%2B1%29%5E2+%2B+3%2A%28x%5E2%2B1%29+-1\".\r\n" );
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document.write( "      So, if I introduce new variable u = \"x%5E2%2B1\", then f(u) = \"u%5E2+%2B+3u+-1\".\r\n" );
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document.write( "Therefore, \"f%28x%5E2-1%29\" = \"%28x%5E2-1%29%5E2+%2B+3%28x%5E2-1%29+-1\" = \"x%5E4+-+2x%5E2+%2B+1+%2B+3x%5E2+-+3+-1\" = \"x%5E4+%2B+x%5E2+-3\".\r\n" );
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document.write( "Answer.  If  \"f%28x%5E2+%2B1%29\" = \"x%5E4%2B5x%5E2%2B3\",  then  \"f%28x%5E2-1%29\" = \"%28x%5E2-1%29%5E2+%2B+3%28x%5E2-1%29+-1\" = \"x%5E4+%2B+x%5E2+-3\".\r\n" );
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