Q2 of 168 Page 231

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

g(x) = –|x + 1| + 3

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.


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