From the course: Preparing for the GMAT

Functions

From the course: Preparing for the GMAT

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Functions

- [Instructor] So in math, function notation might take a little while to wrap your head around if you're not used to it, but it's really just an instruction about what to do with an input to create an output, kind of like in coordinate geometry inputting an x coordinate into an equation of a line to figure out its corresponding y coordinate. So in this video we'll talk about the basics of functions. So if I said to you, f of x equals x squared, that is basically a function. And let me translate this into English 'cause I think it'll maybe make more sense. This basically means on this side, this is like the result of inputting, inputting x. That's what f of x is. And this side is kind of the output. So another way to think about that is if I had an input of two, that would mean that I would get an output of two squared. In other words, four. So you can kind of think of it as the number in these parentheses is what you plug in wherever you see an x on the right side and then that gives you your output which is four. Okay, so these can get a little more complicated. Let me just give you another basic example before I get into a more complicated one. What if we had for the same function, what if we had f of 10? Well, we just pop in a 10 where we see that x so that would be 10 squared or 100. And we could even do this with a variable, what if we had a weird input like f of g, well that would just be g squared. We just put in a g where we see that x, and that's what the function tells us to do so we just square x, whatever x is. Okay, so let me show you a slightly more complicated version of this. What if we had f of x equals x squared and then we also had g of x, a different function that equaled x plus two? Let's say somebody said what is f of g of three. Ugh, that looks pretty complicated, huh? This is actually pretty easy. We work from the inside out, we figure out what g of three is, so if we put in a three over here, where we see the g function, we would get three plus two, so g of three would be three plus two or five, so now that we know that g of three is five, this turns into a five, the g of three we can just rewrite as a five, and we're left with f of five, and we put in a five where we see the x in the f function, and just square it so f of five is 25, so our answer to this complicated-looking question here is just 25. So you may see what we could call a symbol function. And this would be really weird looking but what if we said f star equals f squared plus nine? You might say to yourself well what the heck does a star mean? Well it means anytime we see it next to a number we square that number and add nine. So if I said what is five star equal to, well we have the definition for that, right? We square the number, so we square five and we add nine, so that'll just be 25 plus nine, 34. So symbol functions are just kind of creative ways of portraying the concept of functions so that you might get confused but pretty easy to figure out you still have an instruction on what to do when you see a star next to a number, the instruction is right over here so you just have to plug in a five where you see the f according to that definition. So remember, most function questions just involve following the directions of inputting something and figuring out that output based on what the function tells you to do. If you ever get a composite function, work from the inside out and remember that symbol functions give you instructions just like any other function.

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