Question

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

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

Answer 1

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

As we know from property of mod that $|x+1|\ge 0$

$\Rightarrow -|x+1|\le 0$ (When an inequality is multiplied from $-1$ then it get inverted)

$\Rightarrow -|x+1|+3\le 3$

$\Rightarrow g\left(x\right)\le 3$

This shows that $g\left(x\right)$ will attain maximum value of $3$ and that to when $-|x+1|=0$

i.e. at $x=-1$