Thread: increasing functions prove strictly increasing

Prove: If f and g are increasing functions on an interval I and I is a subset of R, reals . Show that f+g is an increasing function on I. If f is also strictly increasing on I, then f+g is strictly increasing on I.

Originally Posted by apple2010

Prove: If f and g are increasing functions on an interval I and I is a subset of R, reals . Show that f+g is an increasing function on I. If f is also strictly increasing on I, then f+g is strictly increasing on I.

This is not very hard friend.

If then so....

If x ≤ y, then f(x) ≤ f(y) and g(x) ≤ g(y), so (f+g)(x) = f(x) + g(x) ≤ f(y) + g(y) = (f+g)(y)

If x < y, then f(x) < f(y) and g(x) ≤ g(y), so (f+g)(x) = f(x) + g(x) < f(y) + g(y) = (f+g)(y)