document.write( "Question 551941: The function f(x) has the property that f(x+y)= f(x)+f(y)+2xy, for all positive integers x and y. If f(1)=5, then find the value of f(16). \n" ); document.write( "
Algebra.Com's Answer #360003 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "       f(x+y) = f(x) + f(y) + 2xy, f(1) = 5\r\n" );
document.write( "\r\n" );
document.write( "f(2) = f(1+1) = f(1) + f(1) + 2(1)(1) = 5 + 5 + 2 = 12\r\n" );
document.write( "\r\n" );
document.write( "f(4) = f(2+2) = f(2) + f(2) + 2(2)(2) = 12 + 12 + 8 = 32\r\n" );
document.write( "\r\n" );
document.write( "f(8) = f(4+4) = f(4) + f(4) + 2(4)(4) = 32 + 32 + 32 = 96\r\n" );
document.write( "\r\n" );
document.write( "f(16) = f(8+8) = f(8) + f(8) + 2(8)(8) = 96 + 96 + 128 = 320\r\n" );
document.write( "\r\n" );
document.write( "That's the answer, f(16) = 320\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------\r\n" );
document.write( "\r\n" );
document.write( "You weren't asked to find the general solution for\r\n" );
document.write( "\r\n" );
document.write( "f(x) but I found it anyway.\r\n" );
document.write( "\r\n" );
document.write( "It's f(x) = x(x + 4)\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );