document.write( "Question 275302: let f(x)=3x-2x and g(f(x))=2x^2-3x+5. what is g(x)? \n" ); document.write( "

Algebra.Com's Answer #200852 by Edwin McCravy(20056) $\"\"$ $\"About$

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let f(x)=3x-2x and g(f(x))=2x^2-3x+5. what is g(x)?
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document.write( "I think you botched what  equals because  is just ,\r\n" );
document.write( "and if  were merely , then  would just be the same as\r\n" );
document.write( " which would be , and that would be a silly\r\n" );
document.write( "problem.\r\n" );
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document.write( "So I will make up something else for , since I don't believe\r\n" );
document.write( "you really meant . Suppose the problem were\r\n" );
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document.write( "let  and . what is ?\r\n" );
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document.write( "Then  would have to be a quadratic function, say \r\n" );
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document.write( "Then \r\n" );
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document.write( "Rearrange the terms:\r\n" );
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document.write( "Factor x out of the 2nd and 3rd terms on the right\r\n" );
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document.write( "Since , we equate coefficients:\r\n" );
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document.write( "Substitute  into \r\n" );
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document.write( "Substitute  and  into\r\n" );
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document.write( "So \r\n" );
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document.write( "becomes\r\n" );
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document.write( "Edwin

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