Find the domain of the vector function $\mathbf { r } ( t ) = 8 t \mathbf { i } + \frac { 1 } { t - 4 } \mathbf { j }$ .
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 values of $t$ for which $\mathbf{r}(t)$ is defined. In this case, the only possible issue is division by zero in the $\mathbf{j}$ component, which occurs when $t-4=0$, or $t=4$. Therefore, the domain is all real numbers except for $t=4$, which can be expressed as $( - \infty , 4 ) \cup ( 4 , \infty )$. Thus, the answer is choice 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 $\mathbf { r } ( t ) = 8 t \mathbf { i } + \frac { 1 } { t - 4 } \mathbf { j }$