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Q. 3

Expert-verified

Precalculus Enhanced with Graphing Utilities

Found in: Page 556

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Determine the domain of the function
$f (x) = \sqrt{x^{2} - 3 x - 4}$

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

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

Step 2. Find the Domain

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

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

The roots are $x = - 1, 4$ .
So,role="math" localid="1646707378296" $x^{2} - 3 x - 4 \geq 0$ when $x \leq - 1 o r x \geq 4$ .
This implies that the solution set is $\{x | x \leq - 1 o r x \geq 4\}$ .

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