Question 73849
The domain is the set of numbers that are allowed in the function. For instance, for the function {{{1/x}}}, 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 
{{{3/sqrt(10a+1)}}}
So we can say
{{{10a+1>0}}}So we can avoid dividing by 0
{{{10a>-1}}}
{{{a>-1/10}}}
So a must equal -1/10 to have a domain of (-∞10) since if we let x=10
{{{3/sqrt(10(-1/10)+1)}}}
{{{3/sqrt(-1+1)}}}
{{{3/sqrt(0)}}}
{{{3/0}}}Which is not possible, so it shows that everything less than 10 will work. For instance
{{{3/sqrt(8(-1/10)+1)}}}
{{{3/sqrt(-8/10+1)}}}
{{{3/sqrt(0.2)}}}Which can be done since the denominator is greater than zero.