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February 11th, 2015, 09:44 AM   #1
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implicit function

what exactly is implicit function ?
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February 11th, 2015, 09:52 AM   #2
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It's one that cannot be expressed in the form $y = f(x)$.

Instead it is written as $F(x,y) = c$.

For example$$(x + y)\sin xy = 1$$

Actually $y = f(x)$ can be written in this form as $$F(x,y) = f(x)-y = 0$$
so the class of implicit functions includes all explicit functions.

Last edited by v8archie; February 11th, 2015 at 09:57 AM.
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February 11th, 2015, 10:13 AM   #3
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and what are explicit functions ?
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February 11th, 2015, 11:51 PM   #4
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The terms "explicit" and "implicit" describe how you happen to define the function.

For example, $f(x) = x^3$ and $f(x) - x^3 = 0$ define the same function, f(x), but the first definition is explicit and the second implicit. With either method, the function's domain needs to be known.
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February 12th, 2015, 09:16 AM   #5
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i see
so all explicit function is implicit.
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February 12th, 2015, 10:37 AM   #6
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Not exactly. There is no such thing as an implicit function or an explicit function, just an implicit or explicit definition of a function, but some functions are much more easily defined implicitly than explicitly.
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