document.write( "Question 1209317: Let f be a function such that
\n" );
document.write( "f(x+y) = x + f(y) + f(y^2) - y^2
\n" );
document.write( "for any two real numbers x and y. If f(0) = -5, then what is f(1)? \n" );
document.write( "
Algebra.Com's Answer #848307 by mccravyedwin(407)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "Now if you want to change the problem so that f(0) = 0, not -5,\r\n" ); document.write( "then:\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " f(x+y) = x + f(y) + f(y^2) - y^2\r\n" ); document.write( "\r\n" ); document.write( "Let x = -1 and y = 1\r\n" ); document.write( "\r\n" ); document.write( " f(-1+1) = -1 + f(1) + f(1^2) - 1^2\r\n" ); document.write( "\r\n" ); document.write( " f(0) = -1 + f(1) + f(1) - 1\r\n" ); document.write( "\r\n" ); document.write( " 0 = 2f(1) - 2\r\n" ); document.write( "\r\n" ); document.write( " 2 = 2f(1) \r\n" ); document.write( "\r\n" ); document.write( " f(1) = 1\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |