Let $\mathbf { r } ( t ) = \left\{ \sqrt { 2 - t } , \frac { \left( e ^ { t } - 2 \right) } { t } , \ln ( t + 1 ) \right\}$ Find the domain of $r$.
A) $( - 1,0 ) \cup ( 0,2 ]$
B) $( 2 , \infty ]$
C) $[ 2,0 ) \cup ( 0,2 )$
D) $( - \infty , - 1 )$
E) $( - 1,2 ]$

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The Answer of Let $\mathbf { r } ( t ) = \left\{ \sqrt { 2 - t } , \frac { \left( e ^ { t } - 2 \right) } { t } , \ln ( t + 1 ) \right\}$ Find the domain of $r$.
A) $( - 1,0 ) \cup ( 0,2 ]$
B) $( 2 , \infty ]$
C) $[ 2,0 ) \cup ( 0,2 )$
D) $( - \infty , - 1 )$
E) $( - 1,2 ]$

Let r(t)={2−t,(et−2)t,ln⁡(t+1)}\mathbf { r } ( t ) = \left\{ \sqrt { 2 - t } , \frac { \left( e ^ { t } - 2 \right) } { t } , \ln ( t + 1 ) \right\}r(t)={2−t​,t(et−2)​,ln(t+1)}

Let $\mathbf { r } ( t ) = \left\{ \sqrt { 2 - t } , \frac { \left( e ^ { t } - 2 \right) } { t } , \ln ( t + 1 ) \right\}$