Find the maximum and minimum value, f(x) = |x + 2| - 1 - Vidyadip

Question

Find the maximum and minimum value, f(x) = |x + 2| - 1

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Answer

It is given that f(x) = |x + 2| - 1
Now, we can see that |x + 2| $\ge$ 0 for every x $\in$ R
$\Rightarrow f(x)=|x+2|-1 \geq-1$ for every x $\in$ R
Clearly, the minimum value of f is attained when |x + 2| = 0
i.e, |x + 2| = 0
$\Rightarrow$ x = -2
Then, Minimum value of f = f(-2) = |-2 + 2| - 1 = -1
Therefore, function f does not have a maximum value.

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