Function -> Implicit function

In summary, an implicit function is a mathematical function where the dependent variable is not easily isolated on one side of the equation. This makes it different from explicit functions, which have the dependent variable explicitly stated. Examples of implicit functions include circles, ellipses, and conic sections. Implicit functions are important in mathematics and science as they allow us to describe complex relationships and are used in many real-world applications. In calculus, they are used in finding derivatives and for implicit differentiation.
  • #1
roni1
20
0
Hello,
I explain in my class a way to take a function and change it to implict function as:
y - f(x) = 0
I see that way in Wikipedia, so I used it the class.
But my students ask me question that I don't know to answer:
1. Are there more ways to take a function and change it to implict function?
2. Are there infinite ways or a finite ways to do it?

Thanks, for one that answer.
 
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  • #2
1. At least one other way of stating an implicit function: find an inverse.
 

1. What is an implicit function?

An implicit function is a mathematical function where the dependent variable cannot be easily isolated on one side of the equation. This means that the relationship between the independent and dependent variables is not explicitly stated, but rather implied through the equation.

2. How is an implicit function different from an explicit function?

An explicit function has the dependent variable explicitly stated on one side of the equation, making it easier to solve for a specific value. On the other hand, an implicit function has the dependent variable not explicitly stated, making it more difficult to solve for a specific value and often requiring the use of numerical methods.

3. What are some examples of implicit functions?

Some common examples of implicit functions include circles, ellipses, and conic sections. These are all equations where the dependent variable is not explicitly stated, but rather implied through the equation.

4. What is the importance of implicit functions in mathematics and science?

Implicit functions are important in mathematics and science because they allow us to describe complex relationships between variables that cannot be easily expressed using explicit functions. They are also used in many real-world applications, such as modeling physical systems and statistical analysis.

5. How are implicit functions used in calculus?

In calculus, implicit functions are often used in the process of finding the derivative of a function. This is because the derivative of an implicit function can be found by differentiating both sides of the equation with respect to the independent variable. Implicit functions are also used in implicit differentiation, where the dependent variable is treated as an implicit function of the independent variable.

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