SOLUTION: Find (fog)(x) when g(x) = 3/(x - 1), f(x) = (x - 1)/(x - 3) I really need some help

Algebra ->  Functions -> SOLUTION: Find (fog)(x) when g(x) = 3/(x - 1), f(x) = (x - 1)/(x - 3) I really need some help      Log On


   

Question 359067: Find (fog)(x)
when g(x) = 3/(x - 1), f(x) = (x - 1)/(x - 3)
I really need some help
Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+%28x+-+1%29%2F%28x+-+3%29
g%28x%29+=+3%2F%28x+-+1%29
f%28g%29=%28g-1%29%2F%28g-3%29
Let's simplify first.
g-1=3%2F%28x-1%29-1
g-1=3%2F%28x-1%29-%28x-1%29%2F%28x-1%29
g-1=%283-%28x-1%29%29%2F%28x-1%29
g-1=%283-x%2B1%29%2F%28x-1%29
g-1=%284-x%29%2F%28x-1%29
Similarly,
g-3=3%2F%28x-1%29-3
g-3=3%2F%28x-1%29-%283%28x-1%29%29%2F%28x-1%29
g-3=%283-3%28x-1%29%29%2F%28x-1%29
g-3=%283-3x%2B3%29%2F%28x-1%29
g-3=%286-3x%29%2F%28x-1%29
g-3=%283%282-x%29%29%2F%28x-1%29
Put it all together,
f%28g%29=%28g-1%29%2F%28g-3%29
f%28g%29=%28%284-x%29%2F%28x-1%29%29%2F%28%283%282-x%29%29%2F%28x-1%29%29
highlight%28f%28g%29=%284-x%29%2F%283%282-x%29%29%29

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

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



(fog)(x) tells us to substitute 3/(x-1) for every value of x in the f(x) equation

(fog)(x) = %28%28%283%2F%28%28x-1%29%29+-1%29%29%29%2F%28%28%283%2F%28%28x-1%29%29+-+3%29%29%29

(fog)(x) = %28%28%283%2F%28%28x-1%29%29+-1%29%29%29%2F%28%28%283%2F%28%28x-1%29%29+-+3%29%29%29

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

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

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

[3 +(1 -x)]/3(2-x)