document.write( "Question 61871: If f(x)= (2x-3)/5 , find f-1(x) \n" ); document.write( "
Algebra.Com's Answer #42606 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
If f(x)= (2x-3)/5 , find f-1(x)\r\n" );
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document.write( "        2x - 3 \r\n" );
document.write( "f(x) = --------\r\n" );
document.write( "           5\r\n" );
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document.write( "I want you to also learn the graphical significance of\r\n" );
document.write( "inverse as we go, so here is the graph of f(x) in red\r\n" );
document.write( "\"+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+%282x-3%29%2F5%29+\" \r\n" );
document.write( "Replace f(x) by y\r\n" );
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document.write( "     2x - 3 \r\n" );
document.write( "y = --------\r\n" );
document.write( "        5\r\n" );
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document.write( "Interchange x and y\r\n" );
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document.write( "     2y - 3 \r\n" );
document.write( "x = --------\r\n" );
document.write( "        5\r\n" );
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document.write( "Solve for y.\r\n" );
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document.write( "Multiply both sides by 5 to clear of fractions:\r\n" );
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document.write( "5x = 2y - 3\r\n" );
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document.write( "Add 3 to both sides\r\n" );
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document.write( "5x + 3 = 2y\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( " 5x + 3\r\n" );
document.write( "-------- = y\r\n" );
document.write( "    2\r\n" );
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document.write( "or\r\n" );
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document.write( "     5x + 3\r\n" );
document.write( "y = -------- \r\n" );
document.write( "        2\r\n" );
document.write( "  \r\n" );
document.write( "Replace y by f-1(x)\r\n" );
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document.write( "          5x + 3\r\n" );
document.write( "f-1(x) = -------- \r\n" );
document.write( "             2\r\n" );
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document.write( "Now look at the graph of f-1(x) in green:\r\n" );
document.write( "\"+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+0%2C+%285x%2B3%29%2F2%29+\"\r\n" );
document.write( "Now look what happens when we place them on the same \r\n" );
document.write( "set of axes:\r\n" );
document.write( "\"+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+%282x-3%29%2F5%2C+%285x%2B3%29%2F2%29+\"\r\n" );
document.write( "Now watch what happens when we draw the line y = x\r\n" );
document.write( "(That's called the identity line, because y and x are \r\n" );
document.write( "identically equal in the equation y = x. I'll draw it in\r\n" );
document.write( "blue:\r\n" );
document.write( "\"+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+%282x-3%29%2F5%2C+%285x%2B3%29%2F2%2C+x%29+\"\r\n" );
document.write( "Notice that the graph of the green line (the inverse) \r\n" );
document.write( "is the reflection of the original function's graph,\r\n" );
document.write( "drawn in red, across the identity line y=x, drawn in\r\n" );
document.write( "blue.\r\n" );
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document.write( "Edwin
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