Question

if f (x)=|x-1|+x-2|+x-3| when 2 <x <3 is

Answer 1

f(x) = |x-1| + |x-2| + |x-3|

let
p(x) = |x-1|,

q(x) = |x-2| and

r(x) = |x-3|
f(x) = p(x) + q(x)+ r(x)

p(x) = |x -1|
= x-1 for x≥1
= -(x-1) for x<1
Similarly,
q(x) = x-2 for x≥2
= -(x-2) for x<2
r(x) = x-3 for x≥3
= -(x-3) for x<3

Now just see which of the function apply in the given interval 2<x<3

f(x)= p(x)+ q(x)+ r(x)
= (x-1) + (x-2) - (x-3)
= x

Therefore, f(x)= x when 2<x<3.

Hope you understand the approach.
All the best!