Function notation is just a different way of writing a relationship. So on the board behind me, I have f(x) is equal to square root of x plus 2. This is really the exact same thing as y is equal to square root of x equals 2, but just written in a different notation.
So if I said, find y when x is equal to something, you’ll plug that something in, solve it out. Function notation is no different. If I ask you to find f(1), you simply plug in 1 and see what comes up. So here we plug in 1 for x square root of 1 plus 2. Square root of 1 is 1, plus 2 is 3, so this tells us f(1) is equal to 3.
I ask you to find f(5), just plug in 5 for x. Square root of 5 plus 2. Square root of 5 doesn’t simplify to anything, it’s just left as it is. Whatever is right here, is what we plug in. So one of my personal favorite problems is f of smiley face. It’s no different. iI’s a weird symbol, but the idea is exactly the same we just plug whatever is here in for x. So we just get the square root of smiley face plus 2. You probably are never going to do anything like this, but the concept is there.
The last example I want to do with this is, a little bit more involved; f(x+3). We have two things in here which is sort of weird, but the idea is still exactly the same. We plugged in 1, we plugged in 5, we plugged the smiley face. Here we just plug in x+3, so whenever you see x, you plug in x plus 3. So square root x plus 3, and that plus two is still on the outside.
So how we plug in things just like we would with any other function, but here it’s just in a different notation plugging in whenever x is written next to your f. Sometimes they will be represented by a g or an h, it’s all the same thing. It’s just different letters to represent function notation.