# 2. Find the maximum and minimum values, if any, of the following functions given by (ii) $g(x) = - | x + 1| + 3$

Given function is
$g(x) = - | x + 1| + 3$
$-|x+1| \leq 0\\ -|x+1| + 3 \leq 3$       $x \ \epsilon \ R$
Hence, maximum value occurs when -|x + 1| = 0
x = -1
Hence, maximum value occurs at x = -1
and maximum value is
$g(-1) = -|-1+1| + 3 = 3$
It is clear that there is no minimum value  of the given function $x \ \epsilon \ R$

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