algebra 2 help?

Question

For the following, find the composition of functions (fog)(x).
13. g(x) = 3/(x - 1), f(x) = (x - 1)/(x - 3)

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

Answer 1

f(g(x)) = f ( 3/(x-1) )= { 3 / (x - 1) - 1} / { 3/ (x - 1) - 3 }
= { (3 - x + 1) / ( x - 1) } / { ( 3 - 3x + 3) / ( x - 1) }
= (3 - x + 1) / ( 3 - 3x + 3)
= ( 4 - x ) / ( 6 - 3x )
= - ( x - 4) / - ( 3x - 6)
= (x - 4 ) / ( 3x - 6)
so the answer is e

Answer 2

It's asking you to substitute g(x) in place of x in equation f(x), or "f of g of x" fog(x):

f(g(x))= ((3/(x-1)) - 1)/((3/(x-1)-3)
= (3-x+1)/(x-1)/(3-3x+3)/(x-1)
= (4-x)/(6-3x) which is equal to (x-4)/(3x-6)
Answer is E

Answer 3

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

Answer 4

plug g(x) in for x in f(x)... f(g(x)) = (3/(x-1) - 1)/(3/(x-1) - 3)

simplify if necessary and you'll have your answer