Let us see what are explicit and implicit functions okay now to begin with the meaning of explicit and implicit function we first of all start with the word meaning of the word explicit the explicit means to state clearly so explicit function is a function which has something to do it to state clearly okay so the definition of explicit function is such the explicit function is a function in which dependent variable has been explicitly that means clearly stated clearly in terms of an independent variable okay so we can also say it like this that it is a function in which dependent variable is expressed in sum of in in terms of some independent variables okay so what does this exactly means this exactly means that if we denote a function like this Y is equal to F X Y on one side and the terms of X on the other side dependent variable on one side and independent variable on the other side so such type of function can be classified as an explicit function right okay now we are going to go through some examples of explicit function okay so so example of explicit function can be y is equal to e to the power of X plus 1 Y is equal to a X cubed plus BX Y is equal to cos inverse X plus 2 etc .
So all these functions which I have written as explicit function you can see it that Y is on one side and the terms of independent variable is on the other side okay so you can clearly get up at get a get a view get an idea that y is equal to e to the power of X plus 1 so so in all these function y is clearly stated in terms of X okay so whenever you see a function in which bias on the one side and the terms of X are on the other side and you can clearly say Y is equal to this much the function the the dependent variable Y is equal to this much than such a functions you are going to say as explicit functions okay after studying explicit function now we are going to study implicit functions okay so what are implicit function implicit function are just opposite of explicit functions okay the implicit function is a function in which dependent variable has not been explicitly given in terms of independent variables we can also say that it is a function in which dependent variable is not expressed in terms of the independent variables okay so what does this clearly means this this clearly means that if we denote a function like R of X Y that is a real valued function of X Y is equal to 0 okay so our X Y stands for an expression which contains x and y X as an independent variable Y as a dependent variable and it is written equal to 0 . So if a function is stated like this so it can be classified as an implicit function okay now the examples of implicit function can be considered as X square plus y square minus 1 is equal to 0 or X square minus 2xy plus y square is equal to 4 this 4 can always be written on the left hand side as minus 4 so there is no problem regarding this for this book if a function has been written equal to some constant value there or some variable also then this can be written on the left hand side to convert it into a stand form okay and the function y ^ 4 plus X cubed plus 17 is equal to 0 okay so these are all examples of implicit function and the main thing which is clear from these function is this that the value of the dependent variable Y is not clear in terms of the independent variable X you can't make out what is the value of y directly or by just observing the function and sometime the value can be such that it is impossible to solve for y okay so noteworthy point about the implicit function or the importance of the implicit function is the next what we are going to study and there's a final point about the implicit function now the implicit function can be converted into explicit function this is not generally done as the new function that is small this generally complex so to make a expression less complex or in a easier form we use the implicit form of the function okay so this has to be expressed or this should be explained by certain examples I am I'm going to take a example of the equation of the circle so equation of the circle can be written as X square plus y square minus 1 is equal to 0 this is what we have learned okay but if we try to convert it into the implicit 4 into the explicit form okay if you try to convert into explicit form we can write it like this that Y is equal to plus minus square root of 1 minus x squared this one X square goes you're taking square root we are going to get Y is equal to plus minus square root of 1 minus X square okay a new function that is the explicit form of the equation of circle there are two branches one the positive branch if we take plus sign and another negative branch if we take the negative sign okay the explicit form of the equation of a circle gives a complex function okay for our high school level this form of the equation is generally not preferred so that is why we do not convert the equation of the circle in explicit form okay now for a high school student if we are going to explain the branches of the graph so we have to we will have to explain him the theory of many more things so this is going to make the idea of the equation of the circle much more complex okay so for the sake of convenience we often write the function and implicit form and hence we study implicit function and there is the importance of implicit function .