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 February 11th, 2015, 08:44 AM #1 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित implicit function what exactly is implicit function ?
 February 11th, 2015, 08:52 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra 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 08:57 AM.
 February 11th, 2015, 09:13 AM #3 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित and what are explicit functions ?
 February 11th, 2015, 10:51 PM #4 Global Moderator   Joined: Dec 2006 Posts: 19,698 Thanks: 1804 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. Thanks from MATHEMATICIAN
 February 12th, 2015, 08:16 AM #5 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 878 Thanks: 60 Math Focus: सामान्य गणित i see so all explicit function is implicit.
 February 12th, 2015, 09:37 AM #6 Global Moderator   Joined: Dec 2006 Posts: 19,698 Thanks: 1804 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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