# Thread: Need help with composite functions

1. ## Need help with composite functions

What is the difference between (gh)(x) and (g o h)(x)? Is there even a difference or is it the same question in a different format?

2. ## Re: Need help with composite functions

Originally Posted by thebestrose828
What is the difference between (gh)(x) and (g o h)(x)? Is there even a difference or is it the same question in a different format?
it's going to depend on the author

I've seen $(gh)(x) = g(x)h(x)$ as well as $(gh)(x)=g(h(x)) = (g \circ h)(x)$

3. ## Re: Need help with composite functions

fg is the product of the two functions, fog is the composition:
IF f(x)= 3x^3 and g(x)= x^2, fg(x)= (3x^3)(x^2)= 3x^5 and fog(x)= f(g(x))= 3(x^2)^3= 3x^6.

(Yes, some authors, when they are working with the composition only use "fg" to mean the composition. The fact that your textbook uses both notations means that they are intended to be different so that fg is multiplication and fog is the composition.)