document.write( "Question 1037255: Evaluate inverse function of f if f(x)=\"x%5E3%2Bx-1\" \n" ); document.write( "
Algebra.Com's Answer #651975 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
\"f%28x%29=x%5E3%2Bx-1\"\r\n" );
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document.write( "It's a good idea to graph the equation for f(x):\r\n" );
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document.write( "Get some points: (-2,-11), (-1,-3), (0,-1), (1,1), (2,9)\r\n" );
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document.write( "That graph passes both the vertical and horizontal line tests.\r\n" );
document.write( "Therefore it has an inverse which is a function.\r\n" );
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document.write( "The graph of the inverse function will be the reflection of that \r\n" );
document.write( "graph in the green line, which is known as the identity line y=x, \r\n" );
document.write( "where y and x are identical.\r\n" );
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document.write( "To find the equation of the inverse.\r\n" );
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document.write( "1. Replace f(x) by y\r\n" );
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document.write( "\"y=x%5E3%2Bx-1\"\r\n" );
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document.write( "2.  Interchange x and y\r\n" );
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document.write( "\"x=y%5E3%2By-1\"\r\n" );
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document.write( "3. Solve that equation for y.\r\n" );
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document.write( "This involves something pretty advanced.\r\n" );
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document.write( "Write it as\r\n" );
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document.write( "\"y%5E3%2By-1-x=0\"\r\n" );
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document.write( "Substitute in Cardano's formula for the solution\r\n" );
document.write( "to the reduced cubic \"u%5E3%2Ba%2Au%2Bb=0\", which is:\r\n" );
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document.write( "We substitute y for u, 1 for \"a\" and (-1-x) for \"b\".\r\n" );
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document.write( "Simplify what we can\r\n" );
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document.write( "Then we change y to f-1(x)\r\n" );
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document.write( "We get some points, using the calculator\r\n" );
document.write( " (-11,2), (-10,-1.92), (-7,-1.63), (-3,-1), (-1,0), (1,1), (5,1.63),\r\n" );
document.write( "(8,1.92), (9,2), (10,2.07)\r\n" );
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document.write( "Edwin
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