For any a < b, and for any two functions f and g defined on [a, b] which are bounded above on [a, b], prove that, sup{( f + g)(x) ∶ x∈ [a,b ]} ≤ sup{ f(x) ∶ x ∈ [a, b]} + sup{ g(x) ∶ x∈[a,b]}. Giving an example, show that the strict inequality of the above claim can hold.
How to solve this? I find bounds hard
How to solve this? I find bounds hard
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