document.write( "Question 1200539: The function f is defined f(x) = x^2 - 6x + 2 for 0 ≤ x ≤ 3
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Algebra.Com's Answer #834748 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Even though the graph of f(x) = x^2 - 6x + 2 is this:\r\n" );
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document.write( "since , we only use the part between and on the vertical lines \r\n" );
document.write( "at x=0 (the y-axis) and x=3, which is this:\r\n" );
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document.write( "To find the inverse of f(x) = x² - 6x + 2  for 0 < x < 3\r\n" );
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document.write( "1. We replace f(x) by y,\r\n" );
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document.write( "2. We replace x by y and replace y by x:\r\n" );
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document.write( "We solve for y:\r\n" );
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document.write( "Multiply through by -1 to make squared term positive:\r\n" );
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document.write( "Enclose the term that represents \"c\" in parentheses:\r\n" );
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document.write( "Use the quadratic formula:\r\n" );
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document.write( "Now we work out the domain \r\n" );
document.write( "Replace y by what y equals:\r\n" );
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document.write( "Add -3 to all three sides\r\n" );
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document.write( "Since it is between -3 and 0 we use the negative sign\r\n" );
document.write( "for the square root. \r\n" );
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document.write( "That tells us that for the inverse we use the negative\r\n" );
document.write( "sign for the same square root in the inverse:\r\n" );
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document.write( "Going back to the inequality, we square all three sides. \r\n" );
document.write( "Squaring each side involves multiplying each side by \r\n" );
document.write( "itself, which is a negative quantity in the first two, \r\n" );
document.write( "and 0 is multiplied by 0, so we reverse the \r\n" );
document.write( "inequality signs:\r\n" );
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document.write( "Turn it around\r\n" );
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document.write( "Add -7 to all three sides:\r\n" );
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document.write( "That's the domain of the inverse function. So the inverse is\r\n" );
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document.write( "although we write f^-1(x) for y:\r\n" );
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document.write( "  <---ANSWER\r\n" );
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document.write( "Here is the graph of the inverse on the same set of axes (in blue):\r\n" );
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document.write( "And you see that the inverse is the reflection of the original funcetion\r\n" );
document.write( "across the identity line, whose equation is y = x  (where x and y are\r\n" );
document.write( "identically equal and the identity line is the line that bisects the 1st and 3rd\r\n" );
document.write( "quadrants (in green, dashed since it's not part of either graph).\r\n" );
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document.write( "Edwin

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