Constructing g(f(x)) Equation for f(x) = A/(x^2) with Given Conditions"

[sha1000]

Hello everyone,

I need some help (or guidance).

I have an equation f(x) = A/(x²). I need to construct the equation g(f(x)) with following conditions:

- when f(x) -> 0 then g(f(x)) ->1;
- when f(x) -> F_max then g(f(x))->0; (This is important: there is some fixed F_max value at which g(f(x)) =~0.

How shall I proceed?

Thank you

 

[mfb]

I moved the thread to our homework section.

What is F_max?

You don't have to consider f(x) at all with these constraints as you never make conditions on x or similar. Consider this rephrased problem where I just exchanged the letter:
For y->0 you want g(y)->1
For y->F_max you want g(y)->0

It should be easy to find functions that satisfy these conditions.
Afterwards you can plug in f(x) for y.

 

[sha1000]

I moved the thread to our homework section.

What is F_max?

You don't have to consider f(x) at all with these constraints as you never make conditions on x or similar. Consider this rephrased problem where I just exchanged the letter:
For y->0 you want g(y)->1
For y->F_max you want g(y)->0

It should be easy to find functions that satisfy these conditions.
Afterwards you can plug in f(x) for y.

Thank you for your reply. I'll need some time to reformulate the question. There are more elements that must be added to this problem.