Assuming that the derivatives exist.
We know that
so what does that imply about
it is given that f(x) is monotonically increasing and f(g(x)) is monotonically increasing
does g(x) is monotonically increasing??
i tried to solve it this way:
i think that it does.so i want to disprove the theory that g(x) is not is monotonically increasing:
suppose that g(x) is monotonically decreasing
if a<b then g(a)>g(b)
f(a)<f(b)
f(g(a))<f(g(b))
now what??