f (x) = \[-\] | x + 1 | + 3 on R .
Given: f(x) =\[- \left| x + 1 \right|\] + 3
\[- \left| x + 1 \right| \leq 0\] for all x \[\in\] R.
\[\left| x + 1 \right| = 0 . \]
\[ \Rightarrow x = - 1\]
Therefore, the maximum value of f at x = -1 is 3.
Since f(x) can be reduced, the minimum value does not exist, which is evident in the graph also.
Hence, the function f does not have a minimum value.
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