Question

Find the maximum and minimum values, if any, of the following function given by,

$g\left(x\right)=-|x+1|+3$

Answer 1

Given function is $g\left(x\right)=-|x+1|+3$
We know that $|x+1|\ge 0$ for all $xϵR$
$\Rightarrow -|x-1|\le 0$ for all $xϵR\Rightarrow -|x+1|+3\le 3$ for all $xϵR$
The maximum value of g is attained when |x+1| =0
i.e., $|x+1|=0\Rightarrow x=-1$
$\therefore$ Maximum value of $g=g(-1)=-|-1+1|+3=3$
Hence, g(x) has maximum value is at x=-1 but g(x) has no minimum value.