have you seen these sort of questions before yes I thought so these questions are some of the most asked questions in the MTH and maybe it's time that you learn this question once and for all so here we go there are two standard questions and one of them is when you're given a function from the start and then you're asked to either find a of some number or find a solution for f ofx equals some number the other question is when you are given a graph to a function and then the same questions here we go first one saying if you see this little bit it means that y equals F ofx and it almost always is like this when you see f ofx it is the same as y and that's if we're talking about X and Y you can use other variables too of course but it means that if you have this little thing here we know what it tells us about X and Y the whole thing f ofx is the same as y that means that the whole thing here the whole bit on the left side this value is the same as a y not the number two two but the whole thing F of two and because of the equal sign here it means that the left and the right side must must be the same that means that the number six also is the value of y so y equals 6 but the number two it is the number inside of parenthesis and this number always means X if we are talking X and Y so this bit is always X so this information is really a point in the coordinate system it really is the same as writing two and six like this or you can write that so when the x is two then the Y equals 6 so the first question given the information that F ofx = 2X - 3 find F of 2 okay the thing inside the parentheses was the number of X so we know that x equals 2 so this information here the question if you write it you can write it like this find y because the whole thing here was equal to Y so find y if you know that x equals 2 to solve the question we take this bit and replace the x value with the value of two and then we got F of 2 equal 2 * 2 and - 3 so it equals 4 - 3 and this will be the same as number one so the answer to the question here is that f 2 equals 1 fin answer okay so the B question solve F ofx equal 2 and this time I know that this bit is y the whole value of f of x and it tells me that the number two here also is y because the left and the right side is both y the thing that we don't know is the value inside the parenthesis and this is the x value of course it's just X so they had they could have asked a question like this yals 2 find all possible values for X because when you solve an equation sometimes it's more than one possible solution and then we have to find all of them and we take our equation like this and the thing that we do is to replace f ofx with two so we put the number two instead of this bit so 2 equal 2x - 3 and on both sides we add three and I write it only once I write it here so on the right we got 2x only and on the left we got number five and then we divide all sides by two and on on the right we got X and on the left 5 over two or 2.5 is the same thing so the answer to the question is x = 5/ 2 or 2.5 yes book maybe you will ask why we can't use why all the time and that's because if we have some different functions like this it is nice to give them different names and the letter in the function is the name of the function so the first function's name is f next G and the last s in these cases and the letter inside the parentheses it it's there only to tell us which variable the value of f depends on so here the value of x depends on what value X have so if if x is 2 then F will be 2 + 5 7 it depends on the value of x and in the last equation we have t instead of X it's okay we can different variables the value of s depends on what the value of T is here okay and then we have question two as well and this is a graph and the information here is that y on the graph equals F ofx the Y AIS is the this one and X AIS is this one okay so a find F of two now we know that the number two here is the value of x and we will try to find the value of y so it's the same as ask asking this find y if you know that x equals 2 okay so on this graph can you tell me where on the line here where do we have a point that x equals 2 okay say stop stop so here because if we take this point and go to the x-axis we find the number two and in this point we will know the value of y so in this point we go and see what y equals and it equals minus 2 so the answer to the question is that F of two equal - 2 because the answer is the value of y okay so the B question solve f ofx = 2 and then we know that f of x is the whole value of y and the question could be written like this Y = 2 find all possible values for X so on this graph say stop when what y equal 2 not here here's y 3 so say stop stop okay this point here we have number two but we have one point more Soom here we also have number two so this question have two solutions the first one is the value of x here it's minus 2 and the last one is the value of x in this point and it's four so the answers is X1 = - 2 and X2 = 4 okay so then you know this say inside the parenthesis is always X and the whole thing is always the value of why please comment and give you your tips to solve these question and how to think about them bye-bye see you in the next video