determine if the following are correct or wrongso

if correct prove if not then show counter example:

a)if and for then

couldnt find counter example ,i thought f(x)=x but there is not g(x)

to desprove it

b) for x>0

i was told told to use the theore, of lagrange

in which the derivative in some point is the slope between two points

but i dont know how to use it

c)f(x) if bound from the top on (0,1{]}

if f(x) is continues from the left of x=1 then sup f((0,1))>=f(1)

d)if f(x) is integrabile on {[}a,b{]} and if

then there is