Question

How do you find the compositions given `f(x) = x/(x + 1)`, `g(x) = x^2 - 1`?

Answer 1

For f(x) the domain is `R-{1}` and for g(x) is `R` where `R` is the set of real numbers.
Hence

`f(g(x))=(x^2-1)/(x^2-1+1)=(x^2-1)/(x^2)=1-1/(x^2)`

and

`g(f(x))=(x/(x+1))^2-1`