document.write( "Question 987096: How would you \"remove the discontinuity\" of f ? In other words, how would you define f(3) in order to make f continuous at 3? \r
\n" ); document.write( "\n" ); document.write( "f(x) = (x^2 − x − 6)/(x − 3)
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #607873 by ikleyn(52799) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( " $\"f%28x%29\"$ = $\"%28x%5E2+-+x+-+6%29%2F%28x+-+3%29\"$ =           -----> (factorize the numerator) -----> \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "= $\"%28%28x%2B2%29%2A%28x-3%29%29%2F%28x-3%29\"$ = $\"x+%2B+2\"$ . \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "At x=3 you have   x+2 = 5.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So, define   f(3) = 5, and you will have the continuous function.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );