Find the maximum and minimum values, if any, of the following functions given by

Question

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

Philoid · Accepted Answer

It is given that g(x) = –|x + 1| + 3

Now, we can see that –|x + 1| ≤ 0 for every x ϵ R

⇒ g(x) = –|x + 1| + 3 ≤ 3 for every x ϵ R

The maximum value of f is attained when |x + 1| = 0

|x + 1| = 0

⇒ x = -1

Then, Maximum value of g = g(-1) = -|-1 + 1| + 3 = 3

Therefore, function f does not have a minimum value.