Question

f (x) = \[-\] | x + 1 | + 3 on R .

Answer 1

Given: f(x) =\[- \left| x + 1 \right|\] + 3

Now,

\[- \left| x + 1 \right| \leq 0\] for all x \[\in\] R.

\[\Rightarrow\] f(x) = \[- \left| x + 1 \right|\] + 3 \[\leq\] 3 for all x \[\in\] R

\[\Rightarrow\] f(x) \[\leq\] 3 for all x \[\in\] R

The maximum value of f is attained when

\[\left| x + 1 \right| = 0 . \]

\[ \Rightarrow x = - 1\]

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.