Find the domain of the vector function $\mathbf { r } ( t ) = 8 t \mathbf { i } + \frac { 1 } { t - 4 } \mathbf { j }$.
Select the correct answer.
A) $( - \infty , - 4 ) \cup ( - 4 , \infty )$
B) $( - \infty , 8 ) \cup ( 8 , \infty )$
C) $( - \infty , - 8 ) \cup ( - 8 , \infty )$
D) $( - \infty , 4 ) \cup ( 4 , \infty )$

Question

Quizplus · Accepted Answer

The domain of the vector function is the set of all possible input values of $t$ such that the function is defined. Notice that the only potentially problematic part of the function is the $\frac{1}{t-4}$ term, which is undefined when $t=4$. Therefore, we must exclude $t=4$ from the domain.

Hence, the domain of $\mathbf{r}(t)$ is:

$$(-\infty, 4)\cup(4,\infty)$$

which is choice $\boxed{	extbf{(D)}}$.

Find the Domain of the Vector Function r(t)=8ti+1t−4j\mathbf { r } ( t ) = 8 t \mathbf { i } + \frac { 1 } { t - 4 } \mathbf { j }r(t)=8ti+t−41​j

Find the Domain of the Vector Function $\mathbf { r } ( t ) = 8 t \mathbf { i } + \frac { 1 } { t - 4 } \mathbf { j }$