SOLUTION: My question is not just a function it is one that is (f of g)(x) where f(x)= 2/x-8 and g(x)= 7/4x. I thought you put g(x) in for f(x) but how does that work with this problem? Th

Algebra ->  Functions -> SOLUTION: My question is not just a function it is one that is (f of g)(x) where f(x)= 2/x-8 and g(x)= 7/4x. I thought you put g(x) in for f(x) but how does that work with this problem? Th      Log On


   

Question 116512: My question is not just a function it is one that is (f of g)(x)
where f(x)= 2/x-8 and g(x)= 7/4x. I thought you put g(x) in for f(x) but how does that work with this problem? This is from a past test of mine that might be on my final. Thank you so much for your help!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The notation should be f%28g%28x%29%29. Notice that the g%28x%29 replaces the x in f%28x%29, which is what you do with the two function definitions.

f%28x%29=2%2F%28x-8%29 and g%28x%29=7%2F4x

f%28g%28x%29%29=2%2F%28g%28x%29-8%29=2%2F%28%287%2F4x%29-8%29

Of course, now you have to do some simplification
f%28g%28x%29%29=2%2F%28%287-32x%29%2F4x%29
f%28g%28x%29%29=2%2A%284x%2F%287-32x%29%29
f%28g%28x%29%29=%288x%2F%287-32x%29%29

Super-Double-Plus Extra Credit: The domain of f%28x%29 is all reals x%3C%3E8, and the domain of g%28x%29 is all reals x%3C%3E0. What is the domain of f%28g%28x%29%29?