Introduction to Function Notation

Introduction to Function Notation
The Definition of a Function. A full introduction including explanation of the domain and codomain.

[@davidcabreramartinez4892]

it's very very helpful, in my country they don´t understand this stuff very well, however they try to teach it, but it´s wrong and that leads to a lot of misconceptions in this formal math language. thanks ill teach others that don´t understand neither English and maths, for sure.

[@TheMathSorcerer]

:)

[@jeffrey8770]

Hi thanks for the vid it cleared up some concepts for me. But i'm a bit confused because i think i've seen some cases where say, people write ln(x) : R --> R Wouldn't this be incorrect notation because we need every element in the domain (R) needs to be mapped to something in the codomain but obviously since ln(x) only takes positive inputs this is impossible? So would this mean that ln(x) isn't a function from R --> R but actually R>0 --> R (positive reals to reals only) ? Thanks!

[@TheMathSorcerer]

You are correct yes

[@TheMathSorcerer]

You're welcome😄

[@RamanShrikant]

thank you brother! lol im in grade 10 during the summer but i dont mind getting ahead with videos like this to make me more prepared!

[@narendra4114]

Awesome

[@animolwrites6909]

Sir I need advanced set theory solution author Charles c Pinter sir please help me

[@user-amanfeildconvecture]

Sometimes i found definition like there is unique element in B for each A,,,i wants justification that, should 'unique' be there.?

[@user-lb3ex6yh9u]

If f is a function from A to B then each element of A assigns itself uniquely with an element of B. However that doesnt mean each element of A has a different relation with B. Say A= {2,-2,3} and B= {1,2,3,4,5,6,7,8,9} . So a function from A to B f(x)=x² in roster form is given by f={(2,4),(-2,4),(3,9)} Notice 2 things Every element of set A has a relation or allignment with some element of B. The elements of A +2 and -2 are related with same element 4 of B. In this case , f: A->B is a *Many to one* function. But look how no element of A is alligned with 2 elements of B.

[@naeemhaq176]

What is the difference between codomain and range? Aren't they the same thing?

[@devanarayanababu1996]

google it

[@lsdn_Emma]

Thank you

[@TheMathSorcerer]

You're welcome!

[@ian.ambrose]

Hi, thanks for useful video. I have question, is it allowed for function *f* to output Range instead of Codomain?

[@animolwrites6909]

Sir I need advanced set theory book solution author is Charles c Pinter. can you help me

[@chocolatte7736]

Function f will always have a codomain of real numbers. Instead, range is determined by the rule of function f. ex: f: R→R, f(x)=2x+1 interpretation: “Function f such that domain maps onto codomain (all real numbers), f of x equals 2x+1” 2x+1 determines the range, however the domain that is mapped onto the codomain will always be R.

[@ian.ambrose]

@@chocolatte7736 Thank you.

[@DineshSharmaIAS]

Is it for IIT JEE mains & Advance exams in India (country) ?

[@gundappabargalle49]

is that the only reason you study maths?