Composition operator

Hey kiddo! Ever heard of composition? It's like building with Legos, but instead of blocks, we're using functions. And a composition operator is like a special Lego piece that helps us put those functions together in a certain way.

Let's say we have a function that takes a number and returns its square: f(x) = x^2. And we have another function that takes a number and adds 1 to it: g(x) = x+1. Now, if we want to apply g to the output of f (meaning, first we take the square of a number, then we add 1 to it), we can write it like this: g(f(x)). It's like taking the output from f, and feeding it as input to g.

But writing it like that can get pretty messy if we have more functions to compose. That's where the composition operator comes in. It's a symbol that helps us write those compositions more neatly. The composition operator looks like a little circle, and we use it like this: g ◦ f. It means the same thing as g(f(x)), but it's easier to read.

So g ◦ f means "apply f, then apply g to the output of f". And we can also write it like this: (g ◦ f)(x), which means "apply g ◦ f to the input x".

Pretty cool, huh? Now you know how to put functions together like a little Lego master!