SOLUTION: Hi, I'm having some trouble with compositions of functions with fractions. Here is the question: f(x) = (x-1)/(x-3) g(x) = (x-8)/(x-9) Find f(g(x)) Find g(f(x)) Thank yo

Algebra ->  Functions -> SOLUTION: Hi, I'm having some trouble with compositions of functions with fractions. Here is the question: f(x) = (x-1)/(x-3) g(x) = (x-8)/(x-9) Find f(g(x)) Find g(f(x)) Thank yo      Log On


   

Question 360833: Hi, I'm having some trouble with compositions of functions with fractions.
Here is the question:
f(x) = (x-1)/(x-3)
g(x) = (x-8)/(x-9)
Find f(g(x))
Find g(f(x))
Thank you SO much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Computing f(g(x))

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


f%28g%28x%29%29=%28g%28x%29-1%29%2F%28g%28x%29-3%29 Plug in x=g%28x%29 on the right side.


f%28g%28x%29%29=%28%28x-8%29%2F%28x-9%29-1%29%2F%28%28x-8%29%2F%28x-9%29-3%29 Plug in g%28x%29=%28x-8%29%2F%28x-9%29


f%28g%28x%29%29=%28x-8-%28x-9%29%29%2F%28x-8-3%28x-9%29%29 Multiply EVERY term by the LCD x-9 to clear out the fractions.


f%28g%28x%29%29=%28x-8-x%2B9%29%2F%28x-8-3x%2B27%29 Distribute.


f%28g%28x%29%29=1%2F%28-2x%2B19%29 Combine like terms.


I'll let you compute g(f(x))