What is meant by implicit/explicit occurrence of a variable?

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In summary, the conversation discusses the concept of explicit and implicit occurrence of a variable in a given function. The speaker's understanding is that if a function can be expressed solely in terms of a variable, then that variable is explicitly appearing. However, this understanding is questioned in the context of the function f(x)=x^{\frac{1}{3}}+\tanh^{-1}e^x+\sinh(\frac{1}{x})+x^x+x \log x. The speaker also mentions the importance of being able to write any function in the form y=f(x) and the need to "solve for y" to determine its explicit dependence on x.
  • #1
arroy_0205
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I have not understood what precisely is meant when someone says for example, x occurs implicitly or explicitly in a given function. My vague idea is that if f(x) can be expressed solely as a function of x alone then x is said to be explicitly appearing. Is that correct? For exaple in,
[tex]
f(x)=x^{\frac{1}{3}}+\tanh^{-1}e^x+\sinh(\frac{1}{x})+x^x+x \log x
[/tex]
I think x appears explicitly.
What about
[tex]
x^y+y^x=1
[/tex]
I think in this case it is incorrect to say that here x has explicit dependence in y(x). Can anybody make these precise or correct me if I am wrong?
 
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  • #2
We should be able to write any function (of x) in the form y= f(x). In order to determine whether the y in xy+ yx= 1, you have to try to "solve for y". Whether you can or not, y is NOT and "explicit" function of x.
 

FAQ: What is meant by implicit/explicit occurrence of a variable?

What is an implicit occurrence of a variable?

An implicit occurrence of a variable refers to when the variable is used or referenced without being explicitly declared or assigned a value. This can happen when the value of the variable is assumed or inferred from other parts of the code or when the variable is defined in a larger scope outside of the current context.

What is an explicit occurrence of a variable?

An explicit occurrence of a variable refers to when the variable is explicitly declared and assigned a value. This can happen when the variable is defined within the current context or when it is assigned a value through a specific operation or function.

Can a variable have both implicit and explicit occurrences?

Yes, a variable can have both implicit and explicit occurrences within a single codebase. This can happen when the variable is initially declared and assigned a value explicitly, but is then referenced implicitly in other parts of the code.

How do implicit and explicit occurrences affect the value of a variable?

Implicit and explicit occurrences do not necessarily affect the value of a variable, as the value is determined by the most recent assignment. However, they can affect how the variable is used and referenced within the code, as implicit occurrences may not always be obvious and can lead to unexpected results.

How can I prevent implicit occurrences of variables in my code?

To prevent implicit occurrences of variables in your code, it is important to carefully declare and assign values to your variables, and to avoid relying on assumptions or inferred values. It can also be helpful to use variable naming conventions that clearly indicate the purpose of the variable and its scope. Regular code reviews and testing can also help identify any potential implicit occurrences.

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