For every pair of continuous functions `f,g:[0,1]->R` such that `max{f(x):x in [0,1]}= max{g(x):x in[0,1]}` then which are the correct statements

For every pair of continuous functions f,g:[0,1]rarr R such that max{f(x):x in[0,1]}=max{g(x):x in[0,1]} then which are the correct statements

For every pair of continuous function f, g : [0, 1] rarr R such that max {f(x) : x in [0, 1]} = max {g(x) : x in [0, 1]} . The correct statement(s) is (are)

If for a continuous function f,f(0)=f(1)=0,f'(1)=2 and g(x)=f(e^(x))e^(f(x)) then g'(0)=

If f and g are continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

If f and g are continuous functions in [0,1] satisfying f(x) = f(a - x) and g(x) + g(a - x) = a , then int_0^a f(x). g(x) dx is equal to :

If f and g are continuous functions in [0, 1] satisfying f(x) = f(a-x) and g(x) + g(a-x) = a , then int_(0)^(a)f(x)* g(x)dx is equal to