Convert the following absolute value function into piece wise function.
$g (x) = | 2 x + 3 |$

{\begin{matrix} - 2 x + 3 & i f x \geq \frac{- 3}{2} - 2 x - 3 & i f x < \frac{- 3}{2} \end{matrix}

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{\begin{matrix} 2 x - 3 & i f x \geq \frac{- 3}{2} - 2 x + 3 & i f x < \frac{- 3}{2} \end{matrix}

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{\begin{matrix} 2 x + 3 & i f x \geq \frac{- 3}{2} - 2 x - 3 & i f x < \frac{- 3}{2} \end{matrix}

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None of these

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Solution

The correct option is D ${\begin{matrix} 2 x + 3 & i f x \geq \frac{- 3}{2} - 2 x - 3 & i f x < \frac{- 3}{2} \end{matrix}$
$g (x) = | 2 x + 3 |$
$| 2 x + 3 | = 0$
$| 2 x | = - 3$
$| x | = - \frac{3}{2}$
$g (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} 2 x + 3 & i f x \geq \frac{- 3}{2} - 2 x - 3 & i f x < \frac{- 3}{2} \end{matrix}$

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