document.write( "Question 1188640: Is {(x, y)| y^4 = x − 3} a function? \n" ); document.write( "
Algebra.Com's Answer #819766 by ikleyn(52858)\"\" \"About 
You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The answer is   \"highlight%28No%29\".\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "                        EXPLANATION\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For example, for x = 4, we have two values y= 1 and y= -1 both satisfying the equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "But, according to definition of function, the value, corresponding to x= 4 should be UNIQUE.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved and thoroughly explained.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "/////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "By the way,  the given  relation  determines  x  as a function of  y.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "But this relation does not determine  y  as a function of  x.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So,  be alert  ( ! )\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\\\\\\\\\\\\\\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Strictly speaking,  your problem/question is defective :   it asks if the relation determines a function, \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "but does not tell  WHICH  function :   y = y(x)   or   x = x(y).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So,  be alert  TWICE  ( ! )\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );