r(t)= < lnsqrt(t+2) , 4t , t/(9-t^2) >
find the domain of r and answer in interval notation
Will the domain have any brackets or will it all be parenthesis?
The domain of r is determined by the restrictions on each component of r(t).
ln(sqrt(t+2)) requires that the argument of the natural logarithm (t+2) must be positive, which means t+2>0 or t>-2.
4t has no restrictions on the domain.
t/(9-t^2) cannot be undefined, which means 9-t^2 cannot be zero. This equation has solutions of t=3 and t=-3. Therefore, the domain is t<-3 or -3<t<3 or t>3.
In interval notation, the domain is (-∞, -3) ∪ (-3, 3) ∪ (3, ∞).
The domain will have both parentheses and brackets, where parentheses indicate a non-inclusive endpoint and brackets indicate an inclusive endpoint. The domain will have parentheses at -∞, 3, and ∞, and brackets at -3.