Question

How do you find the compositions given `f(x)=7x+4` and `g(x)=x-7`?

Answer 1

`f(x)=7x+4`, `g(x)=x-7`

There can be infinite compositions.

I hope you are talking about the following two compositions.
`(i)` `f(g(x))`
`(ii)` `(g(f(x))`

`(i)` `f(g(x))=f(x-7)=7(x-7)+4=7x-49+4=7x-45`
`implies f(g(x))=7x-45`

`(ii)` `g(f(x))=g(7x+4)=7x+4-7=7x-3`
`implies g(f(x))=7x-3`