on Consider the set C[0,2] of all continuous functions f: [0,2] R with the supremum metric...

 

Transcribed Image Text:

on Consider the set C[0,2] of all continuous functions f: [0,2] R with the supremum metric d(f.g) sup f(x)-g(r)| = max | f(x)= g(x)| => 1[0,2] => 1[0,2] C[0,2]. (You do not have to prove that this is a metric.) Determine d(f,g), where for all r [0,2]. f(x) = 2+ " 9(x) = x [4 marks] on Consider the set C[0,2] of all continuous functions f: [0,2] R with the supremum metric d(f.g) sup f(x)-g(r)| = max | f(x)= g(x)| => 1[0,2] => 1[0,2] C[0,2]. (You do not have to prove that this is a metric.) Determine d(f,g), where for all r [0,2]. f(x) = 2+ " 9(x) = x [4 marks]