document.write( "Question 1170264: Consider the following statement: Let f be a function, such that for all a and b in the domain of f, f(a)=f(b) implies a=b. Then the function f has an inverse.\r
\n" ); document.write( "\n" ); document.write( "Is this statement true or false? \n" ); document.write( "

Algebra.Com's Answer #795125 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " It is TRUE.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Under the given condition, we can define the function g on the set of the images  {b | b = f(a), a belongs to A}  in a way\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    g(b) = a,   if  f(a) = b.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This function is defined correctly on this set and is the inverse function to f.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );