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I still didn't get the difference between implicit and explicit functions. Those examples look same to me.... I mean... y=5x(cubed)-3 can also be written as y-5x(cubed)+3=0. So does converting the example into a func.=0 becomes explicit to implicit?

5 years ago

Answers : (1)

Latika Leekha
askIITians Faculty
165 Points
							Hello student,
As the name suggests, an explicit function is a function in which the dependent variable has been expressed explicitly in terms of independent variable. in other words, we can say that an explicit function is a function in which the dependent variable is expressed in terms of some independent variables.
Eg. y = f(x)
y = 5x3 -3
Implicit function is a function in which the dependent variable has not been expressed explicitly in terms of the independent variable.
Eg. F(x,y) = 0
x2 + y2 – 1 = 0
Yes, it is possible to convert an implicit function into an explicit function but it is not generally done to avoid complexity.
At times, the new explicit function becomes extremely complex and may also give teo different branches of the function.
If we take the example, x2 + y2 – 1 = 0,
y = ± √(1 – x2)
In this function, we can see it clearly that we have obtained two branches of y – one positive and one negative.
5 years ago
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