Find the maximum and minimum value, g(x) = -|x + 1| + 3 - Vidyadip

Question

Find the maximum and minimum value, g(x) = -|x + 1| + 3

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Answer

It is given that g(x) = -|x + 1| + 3
Now, we can see that -|x + 1| $\le$ 0 for every x $\in$ R
$\Rightarrow g(x)=-|x+1|+3 \leq 3$ for every x $\in$ R
The maximum value of f is attained when |x + 1| = 0
|x + 1| = 0
$\Rightarrow x=-1$
Then, Maximum value of g = g(-1) = -|-1 + 1| + 3 = 3
Therefore, function f does not have a minimum value.

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