First slide

Introduction to real valued functions

Question

If $- 4 \leq x < 2$ then $| | x + 2 | - 3 |$ liesintheinterval

Moderate

A

(1, 3]
B

[1, 3]
C

[0, 3]
D

$[0, \infty)$

Solution

We have $- 4 \leq x < 2$
$\begin{array}{l} \Rightarrow - 2 \leq x + 2 < 4 \\ \Rightarrow 0 \leq | x + 2 | < 4 \\ \Rightarrow - 3 \leq | x + 2 | - 3 < 1 \\ \Rightarrow 0 \leq ∥ x + 2 | - 3 | \leq 3 \end{array}$

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