The difference between the maximum and minimum value of the expression $y = | x - 9 | - | x + 2 |$ is

- 11

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0

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11

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22

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Solution

The correct option is D $22$
$y = | x - 9 | - | x + 2 |$
Here the turning points are $- 2, 9$

$y = ⎧ ⎨ ⎩ \begin{matrix} - (x - 9) + (x + 2), & x < - 2 - (x - 9) - (x + 2), & - 2 \leq x < 9 (x - 9) - (x + 2), & x \geq 11 \end{matrix} \Rightarrow y = ⎧ ⎨ ⎩ \begin{matrix} 11, & x < - 2 7 - 2 x, & - 2 \leq x < 9 - 11, & x \geq 9 \end{matrix}$

Here, the maximum value of $y = 11$
Minimum value of $y = - 11$

Hence, the difference $= 11 - (- 11) = 22$

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