finding a compositional function

[pipsy]

In generality the question asked find f(x). however, we only know I(x) and i(x) and the original equation is I = f * i.

This is for homework. However, I don't even understand how to isolate for f. Like does it even make sense to say f = I/i ??

In otherwords I am trying understand the work process behind the algorithm behind the question so to speak I can actually solve the problem.

Thanks!

 

[pka]

In generality the question asked find f(x). however, we only know I(x) and i(x) and the original equation is I = f * i.
This is for homework. However, I don't even understand how to isolate for f. Like does it even make sense to say f = I/i ??
In otherwords I am trying understand the work process behind the algorithm behind the question so to speak I can actually solve the problem.

Unless you post an actual problem, in its exact wording, we cannot help.
It us useless to ask us to guess as what the above quote means.

 

[pipsy]

Unless you post an actual problem, in its exact wording, we cannot help.
It us useless to ask us to guess as what the above quote means.

Sorry, I was just seeing a general way could be used I'll post the exact problem:

i (x) = x/x+6 and I (x) = sqrt3 (x/x+6) find f(x) knowing I= f*i

or is it as simple as saying f(x) = sqrt3 (x) ? or is there a more 'formula based' approach to solving this. The reason I ask is because if we go I(x) = f * i * h and we know the function of i, h and I it becomes quite a bit more harder to infer then first example.

 

[pka]

i (x) = x/x+6 and I (x) = sqrt3 (x/x+6) find f(x) knowing I= f*i

I still can only guess as to what you posted. It looks like
\(\displaystyle \displaystyle i(x)= \frac{x}{{x + 6}}\,\& \,I(x) = \sqrt[3]{{\frac{x}{{x + 6}}}}\) find \(\displaystyle f(x)\) so that \(\displaystyle f\circ i(x)=I(x)\).

If that is it then \(\displaystyle f(x)=\sqrt[3]x\).