Find the domain of vector function $\mathbf { r } = \left( \sqrt { t - 2 } , \ln ( 4 - t ) , \frac { t } { \sqrt { t - 3 } } \right)$
A)[3,4]
B)(3,4)
C)(3,4]
D)(2,$\infty$)
E)[3,4)
F)(-$\infty$,4)
G)(3,$\infty$)
H)[2,$\infty$)

Question

Find the domain of vector function $\mathbf { r } = \left( \sqrt { t - 2 } , \ln ( 4 - t ) , \frac { t } { \sqrt { t - 3 } } \right)$ 
A)[3,4]
B)(3,4)
C)(3,4]
D)(2,$\infty$)
E)[3,4)
F)(-$\infty$,4)
G)(3,$\infty$)
H)[2,$\infty$)

Quizplus · Accepted Answer

The domain is determined by the constraints: $t - 2 \geq 0$, $4 - t > 0$, and $t > 3$. Solving these gives $t > 3$ and $t < 4$, so the domain is $(3, 4)$.

Find the Domain of Vector Function r=(t−2,ln⁡(4−t),tt−3)\mathbf { r } = \left( \sqrt { t - 2 } , \ln ( 4 - t ) , \frac { t } { \sqrt { t - 3 } } \right)r=(t−2​,ln(4−t),t−3​t​)

Find the Domain of Vector Function $\mathbf { r } = \left( \sqrt { t - 2 } , \ln ( 4 - t ) , \frac { t } { \sqrt { t - 3 } } \right)$