Subtracting functions

we're told that f of X is equal to 2x times the square root of 5 minus 4 and we're also told that G of X is equal to x squared plus 2x times the square root of 5 minus 1 and they want us to find G minus f of X so pause this video and see if you can work through that on your own so the key here is to just realize what this notation means G minus f of X is the same thing as G of X minus f of X and so again if this was helpful to you once again I encourage you to pause the video all right now let's work through this again so this is going or I guess the first time but now that we know that this is equal to G of X minus f of X so what is G of X well that's the same thing as x squared plus 2x times the square root of 5 minus 1 and what is f of X well it's going to be 2x times the square root of 5 minus 4 and we are subtracting f of X from G of X so let's subtract this is f of X from G of X and so now it's just going to be a little bit of algebraic simplification so this is going to be equal to this is equal to x squared plus 2x times the square root of 5 minus 1 and now we just have to distribute this negative sign so negative 1 times 2x times the square root of 5 is we're gonna have minus 2x times the square root of 5 and then the negative of negative 4 is positive 4 and let's see if we can simplify this sum so this is going to be equal to we only have one x squared term so that's that one there so we have x squared and let's say we have 2x times the square root of 5 and then we have another oh no we subtract 2x times the square root of 5 so these two cancel out each with each other so those cancel out and then we have minus 1 plus 4 so if we have negative 1 and then we add 4 to it we're going to have positive 3 so if we just fact if we take this and this into consideration 4 minus 1 is going to be equal to 3 and we're done that's what G minus f of X is two x squared plus three