Algebra.Com's Answer #194245 by Edwin McCravy(20055)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
we're supposed to find the inverse of the power function, my teacher is lazy and dosnt teach us much. the answer i got was  he marked it wrong...
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document.write( "First of all, the answer you gave is not a function, with the\r\n" );
document.write( "\"positive or negative\". No function can have a \"±\" in it.\r\n" );
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document.write( "Let's draw the graph of f(x) first.\r\n" );
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document.write( "Now if the domain  weren't given and we just plotted\r\n" );
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document.write( "we'd have this graph:\r\n" );
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document.write( "That graph passes the vertical line test, because no vertical\r\n" );
document.write( "line crosses the graph more than once, so it is a function.\r\n" );
document.write( "However it is not a one-to-one function because it does not\r\n" );
document.write( "pass the horizontal line test. If you draw a horizontal line\r\n" );
document.write( "through it it will cut the graph twice. So it does not have\r\n" );
document.write( "an inverse function.\r\n" );
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document.write( "However since is given for its domain, the graph\r\n" );
document.write( "of f(x) is NOT the one above. Here is the graph of\r\n" );
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document.write( " with the given domain \r\n" );
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document.write( "It consists only of the left half of the graph of \r\n" );
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document.write( "without the given domain \r\n" );
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document.write( "So you see now that the function passes not only the VERTICAL line\r\n" );
document.write( "test, it passes the HORIZONTAL line test as well. So with that\r\n" );
document.write( "restricted domain, it DOES have an inverse. \r\n" );
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document.write( "Now let's sketch the inverse before finding its equation. First draw \r\n" );
document.write( "the line whose equation is  , called the IDENTITY line \r\n" );
document.write( "(because x and y are indentically equal if you have y=x). Let's \r\n" );
document.write( "draw that line. It is a line through the origin which goes at a \r\n" );
document.write( "45° angle to both axes. I'll draw it dotted and in green\r\n" );
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document.write( "Now the inverse of f(x) is the reflection of the graph of\r\n" );
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document.write( "f(x) into that green dotted identity line, whose equation is y=x.\r\n" );
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document.write( "I'll draw it in blue:\r\n" );
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document.write( "The inverse of a function is a function symmetric with the\r\n" );
document.write( "original function's graph about the identity line, y=x.\r\n" );
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document.write( "Now let's find the equation of that inverse.\r\n" );
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document.write( ", x<= 0\r\n" );
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document.write( "1. Change f(x) to y\r\n" );
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document.write( "2. Interchange x and y\r\n" );
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document.write( "3. Solve for y:\r\n" );
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document.write( "Now looking at the graph, the blue inverse graph\r\n" );
document.write( "is entirely below the x-axis. Therefore\r\n" );
document.write( "we can only take the negative square root, \r\n" );
document.write( "and ignore the positive square root.\r\n" );
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document.write( "4. Finally change y to   \r\n" );
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document.write( "So the final answer is\r\n" );
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document.write( "  \r\n" );
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document.write( "Your teacher might expect you to rationalize the denominator.\r\n" );
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document.write( "If so the final answer is\r\n" );
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document.write( "or\r\n" );
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document.write( "Edwin \n" );
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