Question

if f and g are increasing functions on an interval I in R, show that f + g is an increasing function on I. If fi s also strictly increasing on I then f + g is strictly increasing on I. @Number Theory

Answer 1

can we simply say f(x1)< = f(x2) < =.....<=f(xn)
and g(x1) <=g(x2)<=.....<=g(xn)
and f(x1) + g(x1) <=f(x2)+g(x2) <=.....<=f(xn)+g(xn)
and (f + g)(x1) <= (f+g)(x2)<=....<= (f+g)(xn)
so (f+g)(x) is also an increasing function