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

[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?

 

[Mark44]

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.

1. How is a function defined explicitly?

Larson is talking about the domain of a function being defined implicitly or explicitly.

2. How is a function defined implicitly?

See above.

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?