SOLUTION: if f(x)= 9/ (x-6) and g(x)= 3/x, find (f o g)(x) and the domain of f o g. I got 3/(1-2x) but im not sure if thats correct. can you simplify it further? and for my domain i got (x

Algebra ->  Functions -> SOLUTION: if f(x)= 9/ (x-6) and g(x)= 3/x, find (f o g)(x) and the domain of f o g. I got 3/(1-2x) but im not sure if thats correct. can you simplify it further? and for my domain i got (x       Log On


   

Question 929567: if f(x)= 9/ (x-6) and g(x)= 3/x, find (f o g)(x) and the domain of f o g.
I got 3/(1-2x) but im not sure if thats correct. can you simplify it further? and for my domain i got (x cannot equal o,6,.5,) im pretty sure i did the domain incorrectly. Please help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You should have %283x%29%2F%281-2x%29 for your (f o g)(x) when everything is completely simplified.

You'll find that x cannot be zero (due to the division by zero error in g(x)) and that x cannot be 1/2 (due to the division by zero error in (f o g)(x)).

It turns out that x = 6 works just fine in both g(x) and (f o g)(x), so x = 6 is allowed in the domain of the composite function.

The value x = 6 doesn't work in f(x), but that doesn't matter as the x-6 turns into 1-2x when we get to (f o g)(x).