Question

How do you express the following function, f(x) as a composition of two functions f and g `f(x)=x^2/(x^2+4)`?

Answer 1

See explanation below

Explanation:

One way to do it (and I think the simplest) is

`h(x)=x^2` and `g(x)=x/(x+4)`

Then `g(h(x))=g(x^2)=x^2/(x^2+4)`

But note that `h(g(x))=h(x/(x+4))=(x/(x+4))^2=x^2/(x+4)^2` that is different to `g(h(x))`