Hello and welcome to another Easy Math video. In this video we are going to perform operations with functions. We have two functions here, the function F dex which is 5x + 3 and the function gdx which is 2x - 1 and what we are going to calculate is the sum of the functions, the subtraction, both subtractions because F - G is not the same as G - F, the multiplication or product, the division or quotient, which are also two because F / G is not the same as G / F. We are going to do all these operations. They are really very simple, as we will see below. We are going to start with the sum of the two functions. F + G of X is the same as F dex + GX. It is simply adding what FX is worth with what GX is worth. FX is worth 5x + 3. So we put it in and we are going to add what G is worth, which is 2x - 1, then we add 2x - 1 and what we have to do here is simply reduce similar terms. We have 5x + 2x, we have 7x left, and 3 - 1 is left with 2, so 7x + 2 is the result of the function F + G dx that is another function when we calculate the sum function it gives us another function now let's look at the subtraction of functions F - G This will be equivalent to f dex - g dex that is, we write what F of X is worth which is 5x + 3 and we are going to subtract 2x - 1 then we put a minus and in parentheses we put the 2x - 1 since the minus sign is going to affect both terms it is important to put the parentheses because otherwise we would be wrong because we would only have the minus for 2x but -1 we would not be affecting it with the minus what we are going to do now is the multiplication of the minus sign with what is inside here which is really equivalent to changing the sign of both terms then we put the 5x + 3 and we would now have - 2x + 1 whether we see it as multiplication of minus signs by plus minus and minus by minus plus or changing the sign of both terms This one that was positive becomes negative and this one that was negative becomes positive it's the same just like before let's reduce like terms 5x - 2x we have 3x and 3 3 + 1 we have 4 So F - GX is going to be 3x + 4 let's calculate the other subtraction G - F of x to see that it really doesn't make the same difference to us in the case of addition Yes yes it would make the same difference to us the order in which we do the addition doesn't matter but the order of the subtraction does matter So now we have GX - F dex we put the g which is 2x - 1 and now the one we're going to put in parentheses is f we have -5x + 3 in parentheses and what we're going to do is put the 2x - 1 and change the sign of the two terms that are inside here or in other words it will be -5x and -3 that is the result of multiplying the minus sign by the two terms that are here now we're going to perform the reduction of like terms we would have 2x - 5x we have -3x and -1 - 3 we have -4 then G - FX = -3x - 4 now let's look at the multiplication F * GX the multiplication Equal is also going to be multiplying functions and it would be putting the 5x + 3 in parentheses and the 2x - 1 Also in parentheses the parentheses indicate that we are multiplying both functions Now here we have to remember how to do a multiplication of polynomials remember that what we do is take the first term and multiply it by the first term from here 5 * 2 we have 10 and x * x is x cu then we multiply 5x by -1 that is, 5x is multiplied by 2 and then by -1 Then it would be more by men minus and 5x * 1 5x So it remains -5x now we are going to take the 3 and we are also going to multiply it by each one so 3 * 2 we have 6x the x is nothing more is passed and 3 * -1 remains -3 Now we have to reduce similar terms the 10x cu that we pass there is no other term here similar to 10x cu then we do -5x + 6x -5 + 6 we have + 1 so we would have + 1x but remember that 1 is not written just put the pure x and the -3 which also has no similar terms we simply pass it So F * G de X is 10x cu + 2x - 3 now we are going to see the division F by G dex it is the same as putting F dex over GX which can also be written this way as a fraction and what we are going to do is simply write what F dex is worth which is 5x + 3 at the top of a fraction and 2x - 1 would go at the bottom and here there is nothing else to do in some occasions you can simplify the algebraic fraction a bit by factoring and then canceling the factors that are in common but in this case it simply remains like this so F over G of X is 5x + 3 over 2x - 1 and now we are going to see the other division the division G by F dex which is really the same nothing more will remain eh the other way around, that is, it will be GX over FX which is written Like this too and at the top would go g which is 2x - 1 and at the bottom f which is 5x + 3 So G over F dex is 2x - 1 over 5x + 3 and those are all the operations as you can see it is very simple it is simply an algebraic procedure that is performed and well try to perform those same operations that we saw in this video but with these two functions so that you can practice it a little the way in which you are going to learn this is by practicing because then just by watching it you may forget later if you liked the video give it a like Comment if you have any questions or suggestions and subscribe to my channel to receive more videos like this