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Obtaining a function from an equation


Video transcript

for a given input value B the function f outputs a value a to satisfy the following equation for a plus seven B is equal to negative 52 so for given input B the function f the function f will output an A that satisfies this relationship right over here for the a and the B write a formula for f of B in terms of B so what we want to do is we just want to solve for if we're given a B what a does that imply that we have to output or another way to think about it is let's just solve this for a or we could think about a as being a function of B so let's write this so we have for a plus seven B is equal to negative 52 so if I can solve for a in terms of B then any B that I have let's say the B's are on the right-hand side I can put it in I can substitute that value for B and then I can just solve for a I can solve for the a that needs to be outputted so let's do that let's solve for a so I want to get all the a I want I want to just have an a left over on the left hand side I'm going to have everything else on the right hand side including the B's so let's get rid of this B on the left-hand side and I can do that by subtracting 7b of course I want to do that to both sides I can't just do an equation and do an operation only on one side like that so let's subtract and we are left with we are left with the seven B's add up to zero seven B minus 7b and we are left with 4a is equal to negative 52 minus seven B minus 7b now to isolate the a here just have an a here instead of a 4a we can divide both sides by four we can divide both sides by four so I'm just going to divide everything by 4 and on the left hand side we got our goal we are left with an A is equal to now what's negative 54 divided by what's the negative 52 divided by four so let's think about it 52 is 40 plus 12 40 divided by 4 is 10 12 divided by 4 is 3 so it's going to be 13 negative 13 so it's negative 13-7 forts be minus 7/4 be so give it a B if you give me a B I can put that value right over here and then I can calculate what the corresponding a needs to be in order to satisfy this relationship so if I want a formula for F of B in terms of B I could say look you give me a B the output of our function which is f of a the output of our function is going to be is going to be negative 13 minus 7/4 B because the output of our function needs to be an A that will satisfy that will satisfy this equation up here so hopefully that helped