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CCSS.Math:

f of X is equal to 9 minus X actually 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 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 f of X they've given the definition right over there is 9 minus x squared 9 minus x squared and G of X they've given the definition right over here is 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 the 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 this is equal to 9 minus x squared plus since this is a positive we can just 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 zero degree terms and so you have the 9 and you have the 1 + 9 + 1 gets us to 10 so we're done F + G F plus G of X is equal to 4 x squared plus 2x plus 10 notice this is a new function that's created by summing the function definitions of F and G