If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:2:26

Function notation — Basic example

Video transcript

- [Instructor] Let g of x equal x squared minus five. If f of g of x is equal to the square root of x squared plus four, which of the following describes f of x? All right, this is interesting. So one way I could think about doing this is, well, let's just try each of these f of x's. If this was f of x, then f of g of x is going to be equal to, well, everywhere you see an x, you would replace with g of x. So it would be equal to the square root of g of x. G of x plus one. And g of x is x squared minus five. So it'd be the square root of x squared minus five. That's g of x. That's g of x right over there. Plus one. Plus one. And this would be the square root of x squared minus four. X squared minus four. Well, that's not what they have here. They have x squared plus four, so this isn't going to be right. We could try this one. F of, I'll do this in green just for fun. F of g of x is going to be equal to. It's going to be the square root of, well, everywhere you see an x, replace it with a g of x. The square root of g of x plus one. Square root of g of x plus one. Well, that's going to be equal to the square root. G of x is x squared minus one. So g of x is x squared. Oh, wait, let me be careful here. This is gonna be g of x plus nine. G of x plus nine. G of x plus nine, very important detail. We have a nine here. There's gonna be a nine here. And this is going to be equal to the square root of g of x is x squared minus five. X squared minus five. And then you're gonna add nine. You're gonna add nine. Well, what does that give us? This gives us the square root of x squared minus five plus nine. That's going to be plus four, which is exactly what you have right over here. So if f of x is equal to the square root of x plus nine, then f of g of x is going to be this. So that's our choice right over there.