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Expert-verified Found in: Page 556 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Determine the domain of the function$f\left(x\right)=\sqrt{{x}^{2}-3x-4}$

The domain is ${x}^{2}-3x-4\ge 0$.

See the step by step solution

## Step 1. Given Information

The given function is $f\left(x\right)=\sqrt{{x}^{2}-3x-4}$.

## Step 2. Find the Domain

• The square root function is defined for non-negative integers.
• So, ${x}^{2}-3x-4\ge 0$ is the domain.
• Factor the quadratic polynomial on the left-hand side of the equation and find the roots.

$\begin{array}{rcl}{x}^{2}-4x+x-4& =& 0\\ \left(x-4\right)\left(x+1\right)& =& 0\end{array}$

• The roots are $x=-1,4$.
• So,role="math" localid="1646707378296" ${x}^{2}-3x-4\ge 0$ when $x\le -1orx\ge 4$.
• This implies that the solution set is $\left\{x|x\le -1orx\ge 4\right\}$. ### Want to see more solutions like these? 