document.write( "Question 1147866: Find the domain of the f(x) =sqrt(1-x^(x+1)) \n" ); document.write( "
Algebra.Com's Answer #769199 by ikleyn(52915)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Look into the plot of the function  y = x^(x+1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The function is between 0 and 1 in the interval  0 < x <= 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is the domain of your function.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          Plot y = x^(x+1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is informal demonstration, but the formal proof is easy, too.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(1)  The function y = x^(x+1)  is determined for non-negative values of x, ONLY.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2)  If  0 < x <= 1 then  x^(x+1) is OBVIOUSLY less or equal to 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(3)  If      x > 1 ,  then  x^(x+1)  is OBVIOUSLY greater than 1, and the expression under the square root is negative.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "These three positions complete the proof.\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );