What is the difference between an implicit and explicit domain in a function?

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The discussion centers on the distinction between implicit and explicit definitions of a function's domain. An explicit domain is clearly stated, while an implicit domain is inferred from the function's expression. Ron Larson emphasizes that the implied domain includes all real numbers for which the function is defined. The conversation also questions whether Larson provides examples to illustrate these definitions. Understanding these concepts is crucial for accurately defining functions in mathematical contexts.
nycmathguy
Homework Statement
What is the difference between defining a function explicitly and implicitly?
Relevant Equations
n/a
Ron Larson stated:

"The domain of a function can be described explicitly or it can be implied by the
expression used to define the function. The implied domain is the set of all real
numbers for which the expression is defined."

1. How is a function defined explicitly?

2. How is a function defined implicitly?

3. What's the basic difference between the two definitions?
 
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nycmathguy said:
Homework Statement:: What is the difference between defining a function explicitly and implicitly?
Relevant Equations:: n/a

Ron Larson stated:

"The domain of a function can be described explicitly or it can be implied by the
expression used to define the function. The implied domain is the set of all real
numbers for which the expression is defined."
Emphasis added above. Also, your homework statement above doesn't match the Larson quote.
nycmathguy said:
1. How is a function defined explicitly?
Larson is talking about the domain of a function being defined implicitly or explicitly.
nycmathguy said:
2. How is a function defined implicitly?
See above.
nycmathguy said:
3. What's the basic difference between the two definitions?
Does Larson give any examples of functions being defined with implicit domains or explicit domains?
 

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