What do I find difficult?
When I looked at the visual for the composite function of g o f in Figure 9.2, I got really nervous. Holy smokes that looks difficult. At first glance, it looks like a composite function is a function within a function. Or a combination of functions. If you run one function, the output of that function ends up being the input of another function. That's what I understand it to be. If it is really that simple, then I think I got it. But if somehow the functions interact and relate other than that, I'm going to be confused.
With associative functions, h o (g o f) and (h o g) o f are associative if these two functions h o (g o f) and (h o g) o f. This seems to be pretty straight forward. I look forward to learning more about this.
What was interesting to me?
I've always found linear combinations interesting. When there is a combination of functions, I think it provides for interesting opportunities and situations. The composition g o f, defined by (g o f)(a)=g(f(a)) for all a \in A. I think this is a very basic concept, and I look forward to learning more about it. I think we can do some interesting things with it, in finding different functions and looking at the interesting way that things interact. I think we're going to find a fascinating way that functions interact, and I'm excited to learn more about that.
Viva Espana.
When I looked at the visual for the composite function of g o f in Figure 9.2, I got really nervous. Holy smokes that looks difficult. At first glance, it looks like a composite function is a function within a function. Or a combination of functions. If you run one function, the output of that function ends up being the input of another function. That's what I understand it to be. If it is really that simple, then I think I got it. But if somehow the functions interact and relate other than that, I'm going to be confused.
With associative functions, h o (g o f) and (h o g) o f are associative if these two functions h o (g o f) and (h o g) o f. This seems to be pretty straight forward. I look forward to learning more about this.
What was interesting to me?
I've always found linear combinations interesting. When there is a combination of functions, I think it provides for interesting opportunities and situations. The composition g o f, defined by (g o f)(a)=g(f(a)) for all a \in A. I think this is a very basic concept, and I look forward to learning more about it. I think we can do some interesting things with it, in finding different functions and looking at the interesting way that things interact. I think we're going to find a fascinating way that functions interact, and I'm excited to learn more about that.
Viva Espana.
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