Question

Find the maximum and minimum values, if any , of the following functions:
i) $f\left(x\right)=|x+2|-1$
ii) $g\left(x\right)=-|x+1|+3$

Answer 1

$\left(i\right)f\left(x\right)=|x-2|-1$

Minimum value of $|x-2|=0$

Minimum value of f(x)=minimum value of $|x-2|-1$

$=0-1=-1$

Minimum value of $f\left(x\right)=-1\to (x=-2)$

f(x) has no maximum value.

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

$|x+1|>0$

$\Rightarrow -|x+1|<0$

Maximum value of g(x)=maximum value of $-|x+1|+3$

$=0+3=3$

Maximum value of $g\left(x\right)=3$

There is no minimum value of g(x)