document.write( "Question 1190684: Given that f (x)= 3x+4/2x-3 is a one-to-one function,
\n" ); document.write( "(a) find f^-1(-1)
\n" ); document.write( "(b) show f^-1 (f(x))=x
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #822400 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "(a)  To find  f^-1(-1),  you do not need express  f^-1(x) in explicit form : it is UNNECESSARY job.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     What you really need, is to solve equation  f(x) = -1  and find x  in this way;  \r\n" );
document.write( "\r\n" );
document.write( "     then the found value of x will be your answer, i.e. f^-1(-1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     So, I will do it:  I will solve equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         \"%283x%2B4%29%2F%282x-3%29\" = -1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "      To solve, multiply both sides by  (2x-3);  then simplify\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          3x + 4 = -(2x-3)\r\n" );
document.write( "\r\n" );
document.write( "          3x + 4 = -2x + 3\r\n" );
document.write( "\r\n" );
document.write( "          3x + 2x = 3 - 4\r\n" );
document.write( "\r\n" );
document.write( "             5x   =   -1\r\n" );
document.write( "\r\n" );
document.write( "              x   = \"-1%2F5\" = -0.2.      ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  Since it is given in the post that the function f(x) is one-to-one,\r\n" );
document.write( "\r\n" );
document.write( "     the inverse function  f^-1(x) does exist.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     For me, it does not matter now what is its concrete expression.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     But for the inverse function,  the requested identity\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         f^-1 (f(x))=x\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     is valid by the DEFINITION:  so,  THERE IS NOTHING TO PROVE  in this case.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Notice and understand, that my reasoning is absolutely correct in this case: \r\n" );
document.write( "\r\n" );
document.write( "         there is NOTHING TO PROVE: the statement follows immediately from the definition and from the given part.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );