Find the Domain of the Vector-Valued Function Given Below $$\mathbf { r } ( t ) = \sqrt { 16 - t ^ { 2 } } \mathbf { i } + \frac { 1 } { t + 6 } \mathbf { j } + ( t - 4 ) \mathbf { k }$$

Multiple Choice

Find the domain of the vector-valued function given below. $$\mathbf { r } ( t ) = \sqrt { 16 - t ^ { 2 } } \mathbf { i } + \frac { 1 } { t + 6 } \mathbf { j } + ( t - 4 ) \mathbf { k }$$

A) $[ - \infty , 4 )$
B) $[ 0,4 ]$
C) $[ - 4,4 ]$
D) $( - \infty , \infty )$
E) $[ - 4 , \infty )$