Find the domain of the vector function

a$.$ vec$(r)(t)=($:$cost,ln(4-t),\sqrt[\phantom{2}]{t1}$:$)$

b$.$ vec$(r)(t)=($:$\sqrt[\phantom{2}]{4-t^2},e^{-3t},ln(t1)$:$)$

c$.$ vec$(r)(t)=\frac{t-2}{t2}$hat$()sinthat()ln(9-t^2)hat(k)$