Question

If $f\left(x\right)$ is defined in $[-3,3]$ then find the domain of definition of $f(|2x+3|)$

• A. $[-3,0]$
• B. $[-2,0]$
• C. $[-1,0]$
• D. $[0,3]$

Answer 1

The correct option is A $[-3,0]$

For the required domain, $-3\le 2x+3\le 3$

Case 1. $2x+3\ge -3\Rightarrow 2x+3\ge -3\Rightarrow x\ge -3$

Case 2. $2x+3\le 3\Rightarrow 2x+3\le 3\Rightarrow x\le 0$

Hence required domain is $[-3,0]$