document.write( "Question 147723: please show your work on finding the inverse of the function problem
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Algebra.Com's Answer #108170 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
please show your work on finding the inverse of the function problem
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document.write( "First of all, this function is not one-to-one, so its inverse would\r\n" );
document.write( "not be a function.  Here is its graph:\r\n" );
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document.write( "To be one-to-one, a function must not only pass the vertical line\r\n" );
document.write( "test, it also must pass the horizontal line test as well.  As you\r\n" );
document.write( "can see this graph does not pass the horizontal line test.\r\n" );
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document.write( "However we can restrict the domain in two ways, splitting the\r\n" );
document.write( "graph into two separate parts, each of which has an inverse.\r\n" );
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document.write( "If we restrict the function to the interval (, ],\r\n" );
document.write( "we have this graph:\r\n" );
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document.write( "To find the inverse\r\n" );
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document.write( "Change  to \r\n" );
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document.write( "Interchange x and y\r\n" );
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document.write( "Group the \r\n" );
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document.write( "Use the quadratic formula to solve for y:\r\n" );
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document.write( "Now if you just take the +, you have\r\n" );
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document.write( "Change the y to \r\n" );
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document.write( "and the graph of that is:\r\n" );
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document.write( "Now if you put both graphs on the same graph:\r\n" );
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document.write( "Now if you plot the identity line , you see that, the inverse\r\n" );
document.write( "function is the reflection of the original function across the \r\n" );
document.write( "identity line \r\n" );
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document.write( "You can also do the same with the right half of the original graph:\r\n" );
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document.write( "and the equation of that inverse function is\r\n" );
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document.write( "Edwin

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