Find the Domain of the Vector-Valued Function Given Below $\mathbf { r } ( t ) = \mathbf { F } ( t ) \times \mathbf { G } ( t )$

question 32

Multiple Choice

Find the domain of the vector-valued function given below. $\mathbf { r } ( t ) = \mathbf { F } ( t ) \times \mathbf { G } ( t )$ where
$\begin{array} { l } \mathbf { F } ( t ) = t ^ { 3 } \mathbf { i } + \frac { 1 } { t + 4 } \mathbf { j } + ( t - 4 ) \mathbf { k } \\\mathbf { G } ( t ) = \sqrt { 1 - t ^ { 2 } } \mathbf { i } + t \mathbf { j } + ( t - 1 ) \mathbf { k }\end{array}$

• A) \(( - \infty , \infty )\)
• B) \([ - 1,1 ]\)
• C) \([ - 4 , \infty )\)
• D) \([ 0,1 ]\)
• E) \([ 1 , \infty )\)

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