If there are two functions: f(x) and g(x), and the 2nd domain is within the range of the 1st, it can be defined as a new function that associates each element of the domain of f(x) with the value of g[f(x)].
(g o f) (x) = g [f(x)] = g (2x) = 3 (2x) +1 = 6x + 1
(g o f) (1) = 6 · 1 + 1 = 7
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Domain
D(g o f) = {x 
Properties
Associative:
f o (g o h) = (f o g) o h
Not commutative.
f o g ≠ g o f
The identity element is the identity function, i(x) = x.
f o i = i o f = f
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I get it somehow, there are others who are unfamiliar and I have a hard time with it but it’s okay that I get it.
Thanks for sharing your thoughts! It’s completely normal to find some parts unfamiliar or more difficult than others. The important thing is that you’re making progress and understanding more as you practise. Keep going! 😊
At least I understood some of it, but there are others that I’m confused about and have a hard time understanding, but I get it.
Thanks for sharing! It’s great that you’ve understood some of it already. Don’t worry if a few parts are still confusing — keep practising and take your time with the trickier sections. You’ll get there! 😊
The lesson was a little difficult for me, especially the word problems, but the examples helped me understand it better.
Thanks for your feedback! Word problems can definitely be tricky, so we’re glad the examples helped make the lesson clearer. Keep practising — it gets easier with time! 😊
Thankyouuu po