Functional equation in Ext 1/2 (1 Viewer)

[vuhung]

Seen this kind of olympiad-style problem in a top skul's Ext 2 trial exam.

I am not sure if
- Adding these kind of problem into Ext 2 is a good idea? Ext 1 better fit as it is about functions.
- (Stop blaming it is out of syllabus)
- You will encounter these kind of problems in official HSC exams? Pls prove me worng.

 

[oodnadatta01]

Definitely seems like a trial paper type of question. A formal definition of functions, domains to codomains is not taught, and neither is continuity in any appreciable depth other than a definition of limits approaching from both sides and the point x, so saying something like "f is continuous on R" and f: R->R probably wouldn't help students that much. Still a fun question nonetheless.

 

[CirrusTheJet]

This looks like something I might just be able to do. f(y) is just the inverse function of f(x). Is that correct? Or are we defining a new function based on a variable y?

 

[vuhung]

This looks like something I might just be able to do. f(y) is just the inverse function of f(x). Is that correct? Or are we defining a new function based on a variable y?

f(-x) is the value of the function f(x) at -x.
f^-1(x) is the inverse function.
1/f(x), or (f(x))^-1 is a different thing.

 

[vuhung]

Definitely seems like a trial paper type of question. A formal definition of functions, domains to codomains is not taught, and neither is continuity in any appreciable depth other than a definition of limits approaching from both sides and the point x, so saying something like "f is continuous on R" and f: R->R probably wouldn't help students that much. Still a fun question nonetheless.

And your uni is fixing that problem...

A quick check on Cambridge ext 1 text book:
- The definitions of domain, range, continuity, "a continuous function", (and mapping) are given.
- However, a mathematical and formal definitions of those are missing. wth I thought.

 

[oodnadatta01]

And your uni is fixing that problem...

A quick check on Cambridge ext 1 text book:
- The definitions of domain, range, continuity, "a continuous function", (and mapping) are given.
- However, a mathematical and formal definitions of those are missing. wth I thought.

I have no idea if you're agreeing or disagreeing with me or my uni .