Calculus problem set! Please help very confusing

[MaryWill]

I don’t understand what the claims are stating... how would I find if one is false or not? What do these claims mean?

 

[MarkFL]

Here is the image resized and oriented correctly:

 

[Cactusguy]

So, do you know what the notation means?
To translate:
f is a rival of g if there exists an x in the set of real numbers such that for all y in the set of real numbers, x being less than y implies that |f(x)-g(x)| is less than |f(y)-g(y)|
f is a frenemy of g if for all x in the set of real numbers, there exists some y in the set of real numbers such that x is less than y and |f(x)-g(x)| < |f(y)-g(y)|

So that being said, try looking at the problem again. I'll post again later if you still want more help.

 

[Steven G]

Can you please state where you are stuck? For example if you are stuck on part d, then we will not bother to help with the earlier problems. To receive help you need to tell us which problem(s) you need help with and show us your attempt at solving them so we know where you need help.

Do you think that part a is true? If not, come up with two functions that do not live up to it.

 

[Steven G]

Here is the image resized and oriented correctly:

View attachment 13772

Thanks Mark!