To find f o g (x), we need to substitute the function g(x) into the function f(x).
Substituting g(x) into f(x), we have f o g (x) = f(g(x)).
Since g(x) = x + 9/2, we substitute this into f(x):
f o g (x) = f(x + 9/2).
To evaluate this, we replace each occurrence of 'x' in f(x) with (x + 9/2):
f o g (x) = 2(x + 9/2) - 9.
Expanding and simplifying, we get:
f o g (x) = 2x + 9 - 9 = 2x.
So, f o g (x) = 2x.
Now, let's find g o f (x). It involves substituting the function f(x) into the function g(x).
We have g o f (x) = g(f(x)).
Since f(x) = 2x - 9, we substitute this into g(x):
g o f (x) = g(2x - 9).
To evaluate this, we replace each occurrence of 'x' in g(x) with (2x - 9):
g o f (x) = (2x - 9) + 9/2.
Expanding and simplifying, we get:
g o f (x) = 2x + 9 - 9 + 9/2 = 2x + 9/2.
So, g o f (x) = 2x + 9/2.