Hello, I'm having some trouble with this problem any help would be great!
Let I be an interval of the real line, and let f be a real-value function with I is a subset of Dom(f). f is increasing on I iff for all x,y in I, if x<y, then f(x)<f(y). We say f is decreasing on I iff for all x,y in I, if x<y, then f(x)>f(y). Prove that
h is increasing on I, where h=f+g, and f and g are increasing on I.
This is what I have so far, since h,f, and g are increasing then h(x)<h(y), f(x)<f(y), and g(x)<g(y). So h(x)<h(y) = f(x)<f(y) + g(x)<g(y). This is where I'm stuck, can anybody give me some pointers? Thanks!!
Let I be an interval of the real line, and let f be a real-value function with I is a subset of Dom(f). f is increasing on I iff for all x,y in I, if x<y, then f(x)<f(y). We say f is decreasing on I iff for all x,y in I, if x<y, then f(x)>f(y). Prove that
h is increasing on I, where h=f+g, and f and g are increasing on I.
This is what I have so far, since h,f, and g are increasing then h(x)<h(y), f(x)<f(y), and g(x)<g(y). So h(x)<h(y) = f(x)<f(y) + g(x)<g(y). This is where I'm stuck, can anybody give me some pointers? Thanks!!
