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## Q. 2.1

Let $f(t)=f_{1}(t) \mathbf{i}+f_{2}(t) \mathbf{j}=(1 / t) \mathbf{i}+\sqrt{t+1} \mathbf{j}$. Find the domain of $\mathbf{f}$.

## Verified Solution

The domain of $\mathbf{f}$ is the set of all t for which $f_{1}$ and $f_{2}$ are defined. Since $f_{1}(t)$ is defined for $t \neq 0$ and $f_{2}(t)$ is defined for $t \geq-1$, we see that the domain of $\mathbf{f}$ is the set $\{t: t \geq-1$ and $t \neq 0\}$.