Implicit and explicit functions





In mathematics,

The explicit function is a function in which the dependent variable has been given “explicitly” in terms of the independent variable. Or it is a function in which the dependent variable is expressed in terms of some independent variables.

It is denoted by:

y=f(x)

Examples of Explicit functions are:

y=axn+bx where a , n and b are constant.

y=5x3-3

The Implicit function is a function in which the dependent variable has not been given “explicitly” in terms of the independent variable. Or it is a function in which the dependent variable is not expressed in terms of some independent variables.

It is denoted by:

R(x,y) = 0

Some examples of Implicit Functions are:
x2 + y2 – 1 = 0

y4 + x3 +17 = 0

Although you can convert a Implicit function into Explicit function it is generally not done because after conversion
the new explicit function becomes very complex and some times also gives two different function branch.
For example you can convert the first implicit function example above to a Explicit function but after conversion it gives the following function:

y=\pm\sqrt{1-x^2}

And in the new function there are two branches of “y” one the positive branch and another the negative branch.



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