Question

Redefine the function f(x) = |x – 2| + |2 + x|, – 3 ≤ x ≤ 3

Answer 1

Given: function f(x) = |x-2| + |2 + x|, -3≤ x≤ 3

To find: to redefine the given function

Explanation:

We know

when x>0,

|x-2| is (x-2), x≥2

and |2 + x| is (2 + x), x≥-2

when x>0

|x-2| is -(x-2), x<2

and |2 + x| is -(2 + x), x<-2

Now given, f(x) = |x-2| + |2 + x|, -3≤ x≤ 3

It can be rewritten as,

Hence the given function can be redefined as shown above.