Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 1 - Functions and Their Graphs - Chapter Review - Review Exercises - Page 113: 7


The domain is $(- \infty, 2]$

Work Step by Step

In order to compute the domain of the given function, we will first exclude those values of $x$ that will make the function undefined. The square root function is undefined for negative numbers because the square root of a negative number is an imaginary number. So, we can write $2 -x \geq 0 \\ -x \geq -2 \\ x \leq 2$ This shows that the value of $x$ can be any real number less than or equal to $2$. So, the domain is $(- \infty, 2]$
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