 In the Introduction to Functions video, we saw what functions are, we discovered what domain and range mean, and we solved a few functions problems. We saw that you could use any letter, f of x, g of x, any letter, and in this video we're going to look at composite functions, which makes use of different letters. Composite functions are actually used the whole time without people even realizing. So whenever a change in one quantity produces a change in another, which in turn produces a change in a third quantity, we have a composite function. This could be humans cutting down trees in rainforests, which therefore affects orangutan populations. It could be the number of hours you work in a week, which affects your weekly salary, which in turn affects your commission. A composite function is made up of several functions performed in a certain order. The order is really important. Say we have these two functions. Calculate fg of x would be the composite function. It's asking us to put one function into another, and this is where the order really matters. We read backwards for functions. So we put four into g, and then the output of that into f. Whereas if the question had been this, then it'd be asking us to put f into g. So we read right to left for composite functions. So let's go back to that first question. So start with g of four, which gives us five, and then we put five into f, and that's our final answer. Can you now find gf of eight? Make sure you work in the correct order. So put the eight into the f, and then the output of that into the g. Pause the video, solve the question, and click play when you're ready to check. May not always be given a number. The question could just ask us to find fg of x. So then we've got to do some algebraic substitution. So we just substitute 2x minus 3 into f of x in place of any x's. What would gf of x be? Pause the video, work it out, and click play when you're ready. Did you get x minus 3? You don't have to stop at two functions. You can combine as many as you want. Give these questions a go. Pause the video, answer the questions, and click play when you're ready. How did you get on? So there we have composite functions. We can combine multiple functions into one function. You just need to remember to read backwards. So from right to left. Put 2 into f, and then the output of that into g. We'll look at inverse functions and the graphs of functions in other videos. Please like and share our videos with your friends. If you have any questions that you want help with, just comment below.