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\[f(t)\sqrt{t^2+1}\] Find each function value if it exists
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If it is f(t)=sqrt(t^2+1) Then you can say that t^2+1 must be positive or 0, so it can't be negative: t^2+1<0 t^2<-1 but t^2 always positive, so you can say that t can be all real number.
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