Adding functions

f of x is equal to 9 minus x. Actually, it should be 9 minus x squared. And g of x is equal to 5x squared plus 2x plus 1. And then they say find f plus g of x. And this looks a little bit bizarre. What kind of notation is this? And that's really the core of this problem is just to realize that when someone writes f plus g in parentheses like this of x this is just notation for-- so f plus g of x, I just rewrote it. This is the same thing. This is just a kind of shorthand notation for f of x plus g of x. You could view f plus g as a new function that's created by adding the other two functions. But when you view it like this-- so this is really what we have to find. Then, you just have to add these two functions. So f of x, they've given the definition right over there, is 9 minus x squared. And g of x, they've given the definition right over here, is 5x squared plus 2x plus 1. So when you add f of x to g of x, this is going to be equal to-- and I'm just rewriting a lot of things just to make it clear. The f of x part is 9 minus x squared. And then you have the plus. I'll do that in yellow. Plus the g of x part, which is 5x squared plus 2x plus 1. And now we can just simplify this a little bit. We can say-- let me just get rid of the parentheses. I'll just rewrite it. So this is equal to 9 minus x squared plus-- since this is a positive, we don't have to worry about the parentheses. So plus 5x squared plus 2x plus 1. And then we have two x squared terms or second degree terms. We have 5x squared. And then we have negative x squared. 5x squared minus x squared is 4x squared. So you get 4x squared when you combine these two terms. You only have one first degree term 2x there, so plus 2x. And then you have two constant terms, or 0 degree terms. So you have the 9 and you have the 1. And 9 plus 1 gets us to 10. So we're done. f plus g of x is equal to 4x squared plus 2x plus 10. Notice this is a new function that's created by summing the function definitions of f and g.