show that the composition of two increasing functions is increasing

Answer 1

(fog)(x) = f(g(x))
f(x+h) > f(x) if h>0
g(x+h) > g(x) if h>0, so g(x+h) = g(x) + k for some value of k

consider f(g(x+h)). g(x+h) > g(x), so
f(g(x+h)) > f(g(x))

so, increasing