SOLUTION: I have to find the composition of functions! Can't figure this one out either! g(x)=3/(x-1) f(x)=(x-1)/(x-3) find (fog)(x) Again, thanks!!!!!

Algebra ->  Functions -> SOLUTION: I have to find the composition of functions! Can't figure this one out either! g(x)=3/(x-1) f(x)=(x-1)/(x-3) find (fog)(x) Again, thanks!!!!!      Log On


   

Question 214736: I have to find the composition of functions! Can't figure this one out either!
g(x)=3/(x-1) f(x)=(x-1)/(x-3) find (fog)(x)

Again, thanks!!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that is another way of saying f%28g%28x%29%29.



f%28x%29=%28x-1%29%2F%28x-3%29 Start with the given function.


f%28g%28x%29%29=%283%2F%28x-1%29-1%29%2F%283%2F%28x-1%29-3%29 Plug in g%28x%29=3%2F%28x-1%29


Note: this involves replacing 'x' on the left side with g%28x%29 and replacing each 'x' on the right side with 3%2F%28x-1%29.


Multiply EVERY term by the inner LCD x-1 to clear out the inner fractions.


f%28g%28x%29%29=%283-%28x-1%29%29%2F%283-3%28x-1%29%29 Simplify


f%28g%28x%29%29=%283-x%2B1%29%2F%283-3x%2B3%29 Distribute


f%28g%28x%29%29=%28-x%2B4%29%2F%28-3x%2B6%29 Combine like terms.



So