document.write( "Question 82590This question is from textbook
\n" );
document.write( ": For f(x)= 1/x^2-2x-8, find the intervals where f(x)<0 \n" );
document.write( "
Algebra.Com's Answer #59180 by stanbon(75887)![]() ![]() ![]() You can put this solution on YOUR website! For f(x)= 1/x^2-2x-8, find the intervals where f(x)<0 \n" ); document.write( "--------- \n" ); document.write( "f(x) = 1/[(x-4)(x+2)] \n" ); document.write( "--------------- \n" ); document.write( "Comment: f(x) has vertical asymptotes at x=-2 and x=4 \n" ); document.write( "------------- \n" ); document.write( "Draw a number line and mark appropriate points as x=-2 and as x=4. \n" ); document.write( "That breaks the line into three intervals. Check a point in each \n" ); document.write( "interval to see where the solution intervals for your equation lie. \n" ); document.write( "Check (-inf,-2): pick x=100, then f(-100)=1/(-)(-)>0; no solutions there. \n" ); document.write( "Check (-2,4); pick x=0, then f(0) = 1/(-)(+)<0; solution here. \n" ); document.write( "Check (4,inf); pick x=100; then f(100)= 1/(+)(+); no solutions there. \n" ); document.write( "The solution is all vales of x between x=-2 and x=4 but not including \n" ); document.write( "x=-2 and x=4. \n" ); document.write( "Interval notation solution: (-2,4)\r \n" ); document.write( "\n" ); document.write( "================ \n" ); document.write( "Cheers, \n" ); document.write( "Stan H. \n" ); document.write( " |