is this how its done with when evaluating composite functions g*f andf*g?

Question

f(x) = 6 sqrt(x) + 1 ; g(x) = x^2 + 9

is it set up like this to solve?

6 sqrt(x^2+9) + 1 and (6 sqrt(x)+1)^2 + 9

Answer 1

the other way round
g*f = (6 sqrt(x)+1)^2 + 9
and f*g = 6 sqrt(x^2+9) + 1
for gf, you put f(x) for exery x that appears in g
for fg, you put g(x) for every x that appears in x.

Answer 2

Not quite. The functions you have are g∘f and f∘g, but in the wrong order. (g∘f)(x) = g(f(x)) = (6√x+1)²+9 and (f∘g)(x) = f(g(x)) = 6√(x²+9) + 1.

Answer 3

Yes, you seem like you understand the procedure.

Answer 4

it looks correct.... now simplify... ;)