document.write( "Question 886668: Find the inverse of F(x)= -√3x-4. Determine the domain of the original function.
\n" ); document.write( " Determine whether the inverse is also a function, and find the domain and range of the
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Algebra.Com's Answer #536045 by Edwin McCravy(20063) $\"\"$ $\"About$

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document.write( "The other tutor did not give you the correct inverse, because the inverse\r\n" );
document.write( "must have a restricted domain, which he ignored. He stated that the domain\r\n" );
document.write( "of the inverse is \"all real numbers\", but that is wrong. It is necessary that\r\n" );
document.write( "you think of how the graph of the function and its inverse must be.\r\n" );
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document.write( "Here is the graph of \r\n" );
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document.write( "The dotted like is called the \"Identity function\" y=x.  The inverse\r\n" );
document.write( "of a graph is the reflection of the graph in (or across) this dotted\r\n" );
document.write( "line.  Here is the graph of the inverse, in blue, which is the  \r\n" );
document.write( "reflection of the red graph in the dotted identity line (in green).\r\n" );
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document.write( "What the other tutor told you, namely this part:\r\n" );
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\n" ); document.write( "1st: interchange x and y to get::
\n" ); document.write( "x = -sqrt(3y-4)
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\n" ); document.write( "x^2 = 3y-4
\n" ); document.write( "3y = x^2+4
\n" ); document.write( "y = (1/3)x^2 + (4/3)
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document.write( "is correct.  But you cannot stop there.  That's because the graph of\r\n" );
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y = (1/3)x^2 + (4/3)

 is the blue graph below, which\r\n" );
document.write( "extends too far to the left, and the part of that graph that extends\r\n" );
document.write( "into the second quadrant (part of the blue graph left of the y-axis),\r\n" );
document.write( "is NOT part of the inverse and it must be eliminated by restricting\r\n" );
document.write( "the domain of the inverse. The other tutor's error was his failure to \r\n" );
document.write( "restrict the domain. He said \r\n" );
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\n" ); document.write( "Find the domain and range of the inverse.
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which is wrong!!!!\r\n" );
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document.write( "Here is the corrected version:\r\n" );
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document.write( "Original function:\r\n" );
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document.write( "F(x)\r\n" );
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document.write( "Original function's domain: \r\n" );
document.write( "Original function's range:    \r\n" );
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document.write( "Inverse function [when the original function if labeled F(x), the inverse\r\n" );
document.write( "                  function must be labeled F^-1(x).  The other\r\n" );
document.write( "                  tutor just labeled it \"y\".  That's wrong. you must\r\n" );
document.write( "                  change the \"y\" to F^-1(x). \r\n" );
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document.write( "F^-1(x) <--notice the restriction!\r\n" );
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document.write( "Inverse function's domain:   \r\n" );
document.write( "Inverse function's range:  \r\n" );
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document.write( "Notice that the domain of the original function is the same as the\r\n" );
document.write( "range of the inverse function, and the range of the original function\r\n" );
document.write( "is the same as the domain of the inverse function.\r\n" );
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document.write( "Edwin

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