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

[- 3, 0]

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[- 2, 0]

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[- 1, 0]

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[0, 3]

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Solution

The correct option is A $[- 3, 0]$
For the required domain, $- 3 \leq 2 x + 3 \leq 3$
Case 1. $2 x + 3 \geq - 3 \Rightarrow 2 x + 3 \geq - 3 \Rightarrow x \geq - 3$
Case 2. $2 x + 3 \leq 3 \Rightarrow 2 x + 3 \leq 3 \Rightarrow x \leq 0$
Hence required domain is $[- 3, 0]$

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