- #1
amaresh92
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how to identify whether a function is implicit or explicit?
advanced thanks.
advanced thanks.
hunt_mat said:If a function is written (or can be written) as y=f(x) then it is explicit, if it only has the form f(x,y)=0 for example then it is implicit.
hunt_mat said:The equation can be written as:
[tex]
x^{\frac{2}{3}}+y^{\frac{2}{3}}-a^{\frac{2}{3}}=0
[/tex]
So according to my definition, it is implicit. The next question is is, can it be re-arranged to give y=f(x) for some f(x), this requires algebra to check and this is your job.
One way to determine if a function is implicit or explicit is to look at the equation. If the equation is written in the form of y = f(x), then it is an explicit function. If the equation does not have y explicitly written in terms of x, then it is an implicit function.
An explicit function has the dependent variable (usually y) explicitly written in terms of the independent variable (usually x). On the other hand, an implicit function does not have the dependent variable explicitly written in terms of the independent variable.
No, a function can only be either implicit or explicit. It cannot be both at the same time.
To convert an implicit function to an explicit function, you can solve for the dependent variable (usually y) in terms of the independent variable (usually x). This will result in an explicit equation.
Yes, implicit and explicit functions are used in various fields such as economics, physics, and engineering. For example, implicit functions are used to model relationships between variables in economic equations, while explicit functions are used in physics equations to calculate the value of a particular variable at a given time.