February 11th, 2015, 08:44 AM  #1 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 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: 7,232 Thanks: 2411 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: 876 Thanks: 60 Math Focus: सामान्य गणित 
and what are explicit functions ?

February 11th, 2015, 10:51 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,704 Thanks: 1528 
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. 
February 12th, 2015, 08:16 AM  #5 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 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: 18,704 Thanks: 1528 
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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