So, taking the composition of 2 functions, basically taking 1 function plugging it into the other. In general whenever I see this, I don't really like this notation too much so I tend to rewrite it like this because this makes more sense to me going back to function notation but these two statements are saying the exact same thing. This actually just the composition function so it's just telling you to do f of g of x. This is how you do compositions, okay? One quick note is depending on your book, depending on your teacher, you might see this differently, and what you may see is f then a circle g of x. So this is just x+1 squared plus 4 foiling this out, x squared plus 2x plus 1 combining your like te- oops sorry there's +4 in the end, combining all like terms x squared plus 2x plus 5. So what we end up getting is g of x quantity squared plus 4, okay? We know what g of x is, it's x+1. Okay? Just like we had here we've plugged in 2 in to f. So here we're doing is we are taking g of x this inside and plugging into f. So say I come over here we have a little bit more space. We know what f of x is, so this becomes x squared plus 4 plus 1. Okay? So what this happens is this ends up being f of x plus 1, just plugging this in for x. So we look at g, every time we see an x we plug in f of x. Okay? Just like here we had our 2 when we put it into f, the same exact principle here. And what this is really telling us to do is to take f of x and put it into g. So what you will see is something like g of f of x. Okay.Ĭomposition is what happens when we put them together. So this becomes 2 squared plus 4, 2 squared is 4 so this is just 8. If I asked you to find f of 2, you just plug in 2 for x and solve it out. What we're going to do is talk about composition, putting them together, okay? So just a brief reminder. You can evaluate the new combined function h(x) for any value of x. So, you will not always replace x with 2. So behind me I have 2 functions up, f of x and g of x. Unless the function has a restricted domain, you can evaluate the function (including the combined function) for any value of 'x'.
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