## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set: 25

#### Answer

$[2, +\infty)$

#### Work Step by Step

The radicand (expression inside a radical sign) of a square root cannot be negative as its root is an imaginary number. This means that: (1) The radicand of the first radical, which is $x-2$, must be greater than or equal to 0. Thus, $x$ can be any real number greater than or equal o $2$ (2) The radicand of the second radical, which is $x+3$, must be grater than or equal to 0. Thus, $x$ can be any real number greater than or equal to $-3$. Based on (1) and (2) above, the restrictions to the value of $x$ are: (1) $x \ge 2$; and (2) $x\ge -3$ Both of the restrictions above must be satisfied. Thus, the value of $x$ must be greater than or equal to $2$. Therefore, the domain of the given function is $[2, +\infty)$.

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