- #1

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or

[tex]f:\Re \rightarrow \Re[/tex]

[tex]r \rightarrow r^3[/tex]

What are some other ways to define functions? Exotic and extraneous as possible.

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- Thread starter TylerH
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- #1

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or

[tex]f:\Re \rightarrow \Re[/tex]

[tex]r \rightarrow r^3[/tex]

What are some other ways to define functions? Exotic and extraneous as possible.

- #2

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I suppose that you now a cool way to define the function f(x) = ln(x)

- #3

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Yeah, that was my first example. :)

- #4

HallsofIvy

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Actually, [itex]f(x)= x^3[/itex] does NOT define a function because it does not specify the domain. You might well

or

[tex]f:\Re \rightarrow \Re[/tex]

[tex]r \rightarrow r^3[/tex]

What are some other ways to define functions? Exotic and extraneous as possible.

As for the second form, it says too much. You don't have to specify that the range is the set of real numbers because if the domain is the real numbers and the "formula" is [itex]x^3[/itex], the range

If you want an exotic way of defining functions, how about this:

Bessel's function, of order 0 and of the "first kind" is defined as

"The function satisfying Bessel's equation of order 0,

[tex]x^2\frac{d^2y}{dx^2}+ x\frac{dy}{dx}+ x^2y= 0[/tex]

and the initial conditions y(0)= 1, y'(0)= 0."

Or the "Lambert W function" which is defined as

"The inverse function to [itex]f(x)= xe^x[/itex]".

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