document.write( "Question 817173: How do I tell if this equation is one to one f(x)=x²-3x+2 \n" ); document.write( "

Algebra.Com's Answer #491907 by Edwin McCravy(20063) $\"\"$ $\"About$

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How do I tell if this equation is one to one f(x)=x²-3x+2\r
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document.write( "f(x)=x²-3x+2\r\n" );
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document.write( "The best way is first to see if you can prove it isn't one-to-one.\r\n" );
document.write( "If you can you're done.  If you can't, only then try to prove that it\r\n" );
document.write( "is.\r\n" );
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document.write( "Here's how to try to prove it isn't one-to-one:\r\n" );
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document.write( "1.  Choose an arbitrary number in the domain of f(x) to substitute\r\n" );
document.write( "    for x.  Say x=0.\r\n" );
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document.write( "2.  Substitute it for x\r\n" );
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document.write( "    f(0)=(0)²-3(0)+2\r\n" );
document.write( "    f(0)=2\r\n" );
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document.write( "3.  Set the original expression for f(x) equal to the result of step 2.\r\n" );
document.write( "    and solve for x\r\n" );
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document.write( "    x²-3x+2=2\r\n" );
document.write( "      x²-3x=0\r\n" );
document.write( "      x(x-3)=0\r\n" );
document.write( "   x=0;  x-3=0\r\n" );
document.write( "           x=3\r\n" );
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document.write( "4.  If you get another value for x in the domain of f(x), then you\r\n" );
document.write( "    have shown that it is not one-to-one.\r\n" );
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document.write( "    We have shown that f(x) is not one-to-one because both 0 and 3\r\n" );
document.write( "    are in the domain of f(x) and f(0) = f(3) = 2.\r\n" );
document.write( "     \r\n" );
document.write( "    Essentially we have shown that f(x) contains two distinct points \r\n" );
document.write( "    with the same y-coordinate namely (0,2) and (3,2), so it isn't\r\n" );
document.write( "    one-to-one.\r\n" );
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document.write( "Edwin

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