document.write( "Question 698798: Find the value of c such that the domain of f(x) = sqrt(c-x^2) is [-13,13] \n" ); document.write( "

Algebra.Com's Answer #431048 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29+=+sqrt%28c-x%5E2%29\"$ ....if the point is at [ $\"-13\"$ , $\"13\"$ ], means $\"x=-13\"$ and $\"f%28x%29=13\"$ ; so, we will plug it in formula\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+sqrt%28c-x%5E2%29\"$ and solve for $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"13+=+sqrt%28c-%28-13%29%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"13+=+sqrt%28c-169%29\"$ ...both sides raise to power of two\r
\n" ); document.write( "\n" ); document.write( " $\"13%5E2+=+%28sqrt%28c-169%29%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"169+=+c-169\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"169%2B169+=+c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"338=+c\"$ \r
\n" ); document.write( "\n" ); document.write( "so, you have a function $\"f%28x%29+=+sqrt%28338-x%5E2%29\"$ that has a solution set $\"x=-13\"$ and $\"f%28x%29=13\"$ \r
\n" ); document.write( "\n" ); document.write( "let's see it on a graph:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+sqrt%28338-x%5E2%29-13%29+\"$
\n" ); document.write( " \n" ); document.write( "

\n" );