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Find the maximum and minimum values, if any, of the following functions given by g(x) = – | x + 1| + 3

2. Find the maximum and minimum values, if any, of the following functions
given by
(ii) g(x) = - | x + 1| + 3

Answers (1)
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Given function is
g(x) = - | x + 1| + 3
-|x+1| \leq 0\\ -|x+1| + 3 \leq 3       x \ \epsilon \ R
Hence, maximum value occurs when -|x + 1| = 0
x = -1
Hence, maximum value occurs at x = -1
and maximum value is
g(-1) = -|-1+1| + 3 = 3
It is clear that there is no minimum value  of the given function x \ \epsilon \ R

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