Given that the vector function is (t5,4log(t−2),3ln(t+1))
A vector function f(t)=(f1(t),f2(t),f3(t)) is said to be defined if the component functions f1(t)f2(t) and f3(t) are defined.The set of all t for which f1,f2 and f3are defined iscalled the domain of f(t). The \ The component function f2(t)=4log(t−2) is defined only for t−2>0⇒t>2⇒Thedomain of f2(t)is, the set of all t>2. The function f1(t)=t5 is defined for all t∈ R. \\
The component function f3(t)=3ln(t+1) is defined if (t+1)>0⇒ t+1>0⇒t>−1
The domain of f(t) is Domain(f1(t))⋂domain of (f2(t))⋂ Domain of(f3(t)) ⇒ t>0⋂t>2⋂ t>−1
⇒ t>2
Therefore, the domain of the definition of the vector function is t>2.
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