document.write( "Question 1200606: The one-to-one function f is defined below.
\n" ); document.write( "f(x)=9-x^3
\n" ); document.write( "Find f^-1(x), where f^-1 is the inverse of f. \n" ); document.write( "

Algebra.Com's Answer #834776 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The one-to-one function f is defined below.
\n" ); document.write( "f(x)=9-x^3
\n" ); document.write( "Find f^-1(x), where f^-1 is the inverse of f.
\n" ); document.write( "~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Step by step\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "(1)  Write\r\n" );
document.write( "\r\n" );
document.write( "        y = 9 - x^3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2)  Swap x and y in the equation\r\n" );
document.write( "\r\n" );
document.write( "        x = 9 - y^3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(3)  Express \"y\" from this equation\r\n" );
document.write( "\r\n" );
document.write( "        y^3 = 9 - x\r\n" );
document.write( "\r\n" );
document.write( "        y   = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(4)  Stop at this point. You just got  the inverse function.  It is\r\n" );
document.write( "\r\n" );
document.write( "        f^-1(x) = .    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Done.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This methodology (this algorithm) works for any analytical one-to-one function.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " MEMORIZE IT ( ! )\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It works in the same form in thousands other similar cases and problems.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );