Find the maximum and minimum values of the following function given by:
$f (x) = | x + 2 | - 1$

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Solution

$f (x) = | x + 2 | - 1$
Here, $| x + 2 |$ is always greater than $0$ (property of mod)
$| x + 2 | \geq 0$
$\Rightarrow f (x) = | x + 2 | - 1 \geq - 1$
$\Rightarrow$ function has a minimum value of $- 1$ and this happenes when $| x + 2 | = 0$
i.e. at $x = - 2$

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