document.write( "Question 73849: Find the value of a which will ensure that the domain of the function
\n" ); document.write( "f(x) =3/sqrt(ax+1)
\n" ); document.write( "--------------------------------------------------------------------------------
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "is the interval (-¥, 10), i.e. x < 10.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #53158 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
The domain is the set of numbers that are allowed in the function. For instance, for the function \"1%2Fx\", if we plug in x=0 we would get an error since we cannot divide by zero. So x=0 is not in our domain. So we want a value of a that will give us a domain of (-∞,10). To find this value, we need to specify that we cannot get 0 in our denominator or get a negative value in our square root. If we let x=10 we get
\n" ); document.write( "\"3%2Fsqrt%2810a%2B1%29\"
\n" ); document.write( "So we can say
\n" ); document.write( "\"10a%2B1%3E0\"So we can avoid dividing by 0
\n" ); document.write( "\"10a%3E-1\"
\n" ); document.write( "\"a%3E-1%2F10\"
\n" ); document.write( "So a must equal -1/10 to have a domain of (-∞10) since if we let x=10
\n" ); document.write( "\"3%2Fsqrt%2810%28-1%2F10%29%2B1%29\"
\n" ); document.write( "\"3%2Fsqrt%28-1%2B1%29\"
\n" ); document.write( "\"3%2Fsqrt%280%29\"
\n" ); document.write( "\"3%2F0\"Which is not possible, so it shows that everything less than 10 will work. For instance
\n" ); document.write( "\"3%2Fsqrt%288%28-1%2F10%29%2B1%29\"
\n" ); document.write( "\"3%2Fsqrt%28-8%2F10%2B1%29\"
\n" ); document.write( "\"3%2Fsqrt%280.2%29\"Which can be done since the denominator is greater than zero. \n" ); document.write( "
\n" );