compare mathematically

Question

f(x)= √x-2 + √3-x and g(x)= √x-3 + √2-x

Answer 1

Domain of f(x) is: 2 ≤ x ≤ 3; domain g(x) is ø (empty).

So, we can't compare mathematically these functions

Answer 2

1st function

x-2>=0 and 3-x>=0

x>=2 and 3>=x

[2,3] is the domain

2nd function

x-3>=0 and 2-x>=0

x>=3 and 2>=x

x>=3 and x<=2

domain is the empty set