- #1
namekyd
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I Just started Analysis 1 this week and I've encountered some tricky problems in the Assignment
Let f,g : [0,1] -> R be bounded functions.
Prove that inf{ f(x) + g(1-x) : x (element of) [0,1]} >= inf{f(x) : x (element of) [0,1]} + inf{g(x) : x (element of) [0,1]}
Perhaps the triangle inequality?
I know that g(1-x) is still the same function over the same domain as g(x) however it runs in the opposite direction of the original function, thus making f(x) + g(1-x) a different function that f(x) + g(x). I do not know however, how that function is different.
Homework Statement
Let f,g : [0,1] -> R be bounded functions.
Prove that inf{ f(x) + g(1-x) : x (element of) [0,1]} >= inf{f(x) : x (element of) [0,1]} + inf{g(x) : x (element of) [0,1]}
Homework Equations
Perhaps the triangle inequality?
The Attempt at a Solution
I know that g(1-x) is still the same function over the same domain as g(x) however it runs in the opposite direction of the original function, thus making f(x) + g(1-x) a different function that f(x) + g(x). I do not know however, how that function is different.