Let's illustrate what function notation is by starting with an equation y=3x+2. We know this equation can be represented by a straight line graph. If I say what is y when x=1? You would work out that y=5. We can say that y is a function of x, that is, multiply x by 3 then add on 2. The equation is a short way of expressing this. In the same way we can use f(x), that is, a function of x, or f of x, where f(x)=3x+2. Instead of asking what is y when x=1, we can write f(1)=? It's shorthand. But it's more than that. Suppose we write z=2y-1 and y=3x+2 and ask the question what is z when x=1? First you work out y, which we know is 5, then we would put y=5 into z=2y-1 and z would be 9. Using function notation and writing g(y)=2y-1 is the same as z=2y-1. But here's the clever bit: we can also write g(f(x)) or gof(x) or g of f(x) to mean the same. Shorthand again. gof(1)=9. We would also have written g(x)=2x-1 instead of g(y)=2y-1. This shorthand function notation means we won't run out of letters like x, y, z, because we can simply write our functions in terms of x and leave it at that. And you can write things like f(x)+g(x) or h(x)=(f(x)+g(x))/(f(x)-g(x)). It's a whole new world! You still need to work out the answers with as much effort as before, but it's easier to express the question. And in some cases there are quicker ways to get the answer. I hope this helps.