Functions help?

Question

I have a function problem that I just timply cannot solve, ive been trying for days but I can't make anysense of it.

F(g(x))

g(x) = 3/(x - 1), f(x) = (x - 1)/(x - 3)

A(x - 1)/(x - 3) * 3/(x - 1) - Wrong
B(x - 1)/(x - 1) * 3/(x - 1)
C(x - 4)/(x - 2) - Wrong
D(x - 4)/(3x - 3)
E(x - 4)/(3x - 6)
F3x^2 - Wrong

The ones marked - wrong have already been told by my teacher that they are incorrect. But which one is the right one and how to I solve this one?

Its actually F compsed of G not just g.

(f o g)(x)

Answer 1

y = g(x) = 3/(x - 1)

f(y) = (y-1)/(y-3)

NUMERATOR:
[3/(x-1)] - 1

= [3/(x-1)] - [(x-1)/(x-1)]

= [3 - (x-1)] / (x-1)

= (4-x)/(x-1)

DENOMINATOR:
[3/(x-1)] - 3

= [3/(x-1)] - [(3x-3)/(x-1)]

= [3 - (3x-3)] / (x-1)

= (6 - 3x)/(x-1)

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

f(g(x)) = (4 - x) / (6 - 3x)

Looks like E is the same as what I have, if you multiply by 1 in the form of [-1] / [-1]. Go with that one.

Answer 2

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

(x-4)/(3x-6) (E)