For every pair of continuous functions f ,   g   : 0 ,   1 → R such that max ⁡ f x : x   ∈ 0 ,   1 = max ⁡ { g x   : x   ∈ 0 ,   1 } , then the correct statement (s) is (are)

Question

For every pair of continuous functions f , &#160; g &#160; : 0 , &#160; 1 &#8594; R such that max &#8289; f x : x &#160; &#8712; 0 , &#160; 1 = max &#8289; { g x &#160; : x &#160; &#8712; 0 , &#160; 1 } , then the correct statement (s) is (are)

Aicharya · Accepted Answer

Let f x and g x achieve their maximum value at x 1 and x 2 respectively h x = f x - g x h x 1 = f x 1 - g x 1 ≥ 0 h x 2 = f x 2 - g x 2 ≤ 0 ⇒ h c = 0 where c ∈ 0 , 1 ⇒ f c = g c .

For every pair of continuous functions f ,   g   : 0 ,   1 → R such that max ⁡ f…

Solution

For every pair of continuous functions f , &#160; g &#160; : 0 , &#160; 1 &#8594; R such that max &#8289; f…

Solution

For every pair of continuous functions f , g : 0 , 1 → R such that max ⁡ f…