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 f(x) = |x + 2| – 1

Philoid · Accepted Answer

It is given that f (x) = |x + 2| – 1

Now, we can see that |x + 2| ≥ 0 for every x ϵ R

⇒ f (x) = |x + 2| – 1 ≥ -1 for every x ϵ R

The minimum value of f is attained when |x + 2| = 0

|x + 2| =0

⇒ x = -2

Then, Minimum value of f = f(-2) = |-2 + 2| - 1 = -1

Therefore, function f does not have a maximum value.