The domain of the vector function $\mathbf { v } ( t ) = 2 ^ { t } \mathbf { i } - 5 t ^ { 2 } \mathbf { j } + \log _ { 2 } ( t - 4 ) \mathbf { k }$ is
A) $( 4 , \infty )$
B) $( - 4 , \infty )$
C) $( - \infty , - 4 )$
D) $( - \infty , - 4 ) \cup ( 4 , \infty )$
E) $( - 4,4 )$

Question

Quizplus · Accepted Answer

The domain is determined by the restrictions on $t$ from each component of the vector function. $2^t$ is defined for all real numbers, and $-5t^2$ is also defined for all real numbers. The restriction comes from $\log_2(t-4)$, which requires $t-4 > 0$, or $t > 4$. Therefore, the domain is $(4, \infty)$.

The Domain of the Vector Function v(t)=2ti−5t2j+log⁡2(t−4)k\mathbf { v } ( t ) = 2 ^ { t } \mathbf { i } - 5 t ^ { 2 } \mathbf { j } + \log _ { 2 } ( t - 4 ) \mathbf { k }v(t)=2ti−5t2j+log2​(t−4)k

The Domain of the Vector Function $\mathbf { v } ( t ) = 2 ^ { t } \mathbf { i } - 5 t ^ { 2 } \mathbf { j } + \log _ { 2 } ( t - 4 ) \mathbf { k }$