Question

find f o g (x) and g o f (x) when
f(x)=2x-9 and g(x)=x+9/2

Answer 1

I'll do one you do the other
f o g (x)
= f(g(x))
= f(x+9/2)
= 2(x + 9/2) - 9
= 2x + 9 - 9
= 2x

I worked on the assumption that you meant what you typed for g(x)
If, however, you meant g(x) = (x+9)/2 , you will have to make the appropriate changes.
The process will remain the same.

Answer 2

thank you
that's what I got

Answer 3

I suspect that it was (x+9)/2
In that case, f and g are inverses, and f◦g = g◦f = x