Question

Find the domain of the function $f\left(t\right)=\sqrt{t+1}$.

Short answer

The domain$\left(D_f\right)$ of the function is $t\in [-1,\infty )$.

Step-by-step solution

Step 1. By definition of domain of a function.

The given function is $f\left(t\right)=\sqrt{t+1}$. Now, by definition of domain of function, the domain of the function is defined for all real values of$\left(t\right)$ for which the function is defined.

Step 2. By definition of domain of square root function.

From the square root function $f\left(t\right)=\sqrt{t+1}$, the domain is defined for all real numbers $\left(t\right)$for which the expression inside the square root is greater than or equal to zero.

role="math" localid="1644580287740" $\begin{array}{c}t+1\ge 0\text{\hspace{0.17em}gives}\\ t\ge -1\end{array}$

Hence the domain of the function is$t\in [-1,\infty )$

Step 3. Description of steps.

The domain of the function is $t\in [-1,\infty )$.