document.write( "Question 1178867: Determine which two functions are inverses of each other.
\n" ); document.write( "F(x)= 9x G(x)=(x)/(9) H(x)=(9)/(x) \n" ); document.write( "
Algebra.Com's Answer #808361 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "She's right except she didn't tell you that one of those, H(x) is ITS OWN\r\n" );
document.write( "inverse!  Yes, that's right!  A function can be its own inverse.\r\n" );
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document.write( "She showed you how to find inverses by four steps, although she only\r\n" );
document.write( "mentioned step 2, and assumed you knew the other 3 steps.\r\n" );
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document.write( "1. Replace F(x), G(x), or H(x), by y, respectively.\r\n" );
document.write( "2. Interchange x and y.\r\n" );
document.write( "3. Solve for y.\r\n" );
document.write( "4. Replace y by F-1(x), G-1(x), or H-1(x), respectively.  \r\n" );
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document.write( "Let's follow those 4 steps with H(x)=9/x\r\n" );
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document.write( "    H(x)=9/x\r\n" );
document.write( "1.     y=9/x\r\n" );
document.write( "2.     x=9/y\r\n" );
document.write( "3.    xy=9\r\n" );
document.write( "       y=9/x\r\n" );
document.write( "4. H-1=9/x  \r\n" );
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document.write( "How about that! H(x) and H-1(x)=9/x both equal 9/x, so\r\n" );
document.write( "that means H(x) is ITS OWN inverse!\r\n" );
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document.write( "She also didn't show you what the graph of a function and its inverse look\r\n" );
document.write( "like graphically.\r\n" );
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document.write( "I will draw F(x)=9x in blue, G(x)=x/9 in green, on the same set of axes and\r\n" );
document.write( "also a dotted graph in red of y=x, which is a line that goes 45° through the\r\n" );
document.write( "origin. It's often called the \"IDENTIty line\" because its equation, y=x,\r\n" );
document.write( "shows that it is the case where y and x are IDENTIcal.\r\n" );
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document.write( "Notice that F(x) and G(x), which are INVERSES are REFLECTIONS of EACH OTHER\r\n" );
document.write( "in (or across) the dotted IDENTIty line.\r\n" );
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document.write( "Any function's graph and its inverse's graph are always REFLECTIONS of EACH\r\n" );
document.write( "OTHER in (or across) the IDENTIty line. \r\n" );
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document.write( "Now let's draw the graph of H(x) in green, and also the identity line y=x:\r\n" );
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document.write( "See how the graph is ITS OWN REFLECTION in (or across) the dotted\r\n" );
document.write( "IDENTITY LINE? H(x) is ITS OWN INVERSE!\r\n" );
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document.write( "Edwin
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