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Expert-verified Found in: Page 157 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Find the domain of the function $f\left(t\right)=\sqrt{t+1}$.

The domain $\left({D}_{f}\right)$ of the function is $t\in \left[-1,\infty \right)$.

See the 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 $t\in \left[-1,\infty \right)$

## Step 3. Description of steps.

The domain of the function is $t\in \left[-1,\infty \right)$. ### Want to see more solutions like these? 