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?
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.)