To find composite functions, sub the 'most behind' function into the function to front . For eg. gf(x): sub f(x)'s entire equation into x of g(x).For fg(x), it's the opposite (g into f)

For comment I think is to evaluate whether these functions exists.
To determine whether a composite function exists:
For eg. gf(x).
Think of functions as washing machines and dryers. The behind function f(x) as washing machines and front function dryers g(x).
So, the dirty clothes (domain of f) goes through f first cause you need to wash the clothes first and then it's range is washed clothes which is also the input for the dryer g(x).
gf doesn't exist if there are washed clothes (range of f) can't go into the dryer g(x).(domain of g) = Rf not subset of Dg.
gf exist if the washed clothes (range of f) can go into dryer g(x)(domain of g) = Rf is a subset of Dg.

If you want to memorize it's just range of behind function (subset= exist/not subset =does not exist) domain of front function. However, I highly suggest trying to understand the logic behind it because this analogy can help finding composite functions range without drawing out (saves a lot of time) and enables you to do composite functions involving piecewise functions.

Hope this helps! ;)) I was in your position two years ago haha jia youu!