A question about functions?

Question

I got a question that is surprisingly simple but for some reason I just can't figure it out. Its beyound me, I don't know why, can anybody help me?

The problem is: (fog)(x):
g(x) = 3/(x - 1), f(x) = (x - 1)/(x - 3)

Yes (fog)(x) would be f(g(x))

Answer 1

g(x) = 3 / (x-1)
f(g(x)) = [3/(x-1) - 1] / [3/(x-1) - 3] = (3 - x + 1)/ (3 - 3x +3)
= (4 - x) / (6 - 3x)

Answer 2

do you mean f(g(x))?
if that is the case, then
f(g(x))= (3/(x-1)-1)/(3/(x-1)-3)
it is just plugging the function in another function.
to make it more clear, use f(x)=x^2 and g(x)=3x for example
f(g(x))=f(3x)=(3x)^2
g(f(x))=g(x^2)=3x^2