SOLUTION: Find the value of a which will ensure that the domain of the function f(x) =3/sqrt(ax+1) ----------- ----------- ----------- ----------- ----------- ----------- --------

Question 73849: Find the value of a which will ensure that the domain of the function
f(x) =3/sqrt(ax+1)
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is the interval (-�, 10), i.e. x < 10.

Answer by jim_thompson5910(35256) (Show Source): 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 , 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

So we can say
So we can avoid dividing by 0

So a must equal -1/10 to have a domain of (-∞10) since if we let x=10

Which is not possible, so it shows that everything less than 10 will work. For instance

Which can be done since the denominator is greater than zero.
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