Question

Is inverse a functional? From what I learned, a functional is a function which you input a function and output a real number and inverse does exactly that. So by definition, inverse should be considered as a functional. But why nobody mention that?

Answer 1

we dont call it functional, we call it a function

Answer 2

ok, @perl , so what is classified as a functional, then?

Answer 3

it is just called a function

Answer 4

What we are doing is, you are given a function. then you are asked , is the inverse *relation* a function. The inverse relation just switches the x and y values , it is not necessarily a function

Answer 5

the inverse relation may or may not be a function itself

Answer 6

the inverse relation is defined as switching x and y values.
for example suppose you have a function

f = { (1,2) ( 1,3) (2,3) (4,5) }

the inverse relation , we can call it f^-1

f^-1 = { (2,1) (3,1) (3,2) (5,4) }

but f^-1 is not a function

Answer 7

ok, but can you give an example of functional? @perl

Answer 8

an example of a function whose inverse relation is also function? sure, all you need is a one to one function.

f = { (1,2) (2,3 ) (3,4) (4,5) }

f^-1 = { (2,1) (3,2 ) (4,3 ) (5,4 ) }

And with functions, f(x) = x^3 , the inverse relation f^-1 = x^(1/3) is also a function

Answer 9

please stop using the word functional

Answer 10

functions, if you are using english.

Answer 11

http://en.wikipedia.org/wiki/Functional_(mathematics)

Answer 12

take a look

Answer 13

you are studying this?

Answer 14

I could not understand partially because my mother language is not englsih

Answer 15

yes

Answer 16

this is advanced math ,

Answer 17

I know

Answer 18

I;ve done cal III

Answer 19

your question was, is the inverse a functional. so my question is, inverse of what?

Answer 20

you didnt use the definition of functional
"Is inverse a functional? From what I learned, a functional is a function which you input a function and output a real number and inverse does exactly that. So by definition, inverse should be considered as a functional. But why nobody mention that?"

Answer 21

ok. so how do I apply that

Answer 22

no idea. why are you interested in functionals?

Answer 23

you dont learn about functionals in isolation, its part of some analysis course, possibly

Answer 24

I want to do calculus of variations

Answer 25

oh ok

Answer 26

my sarting oint is physics, more specifically, Lagrangian mechanics

Answer 27

then you better start with an intro to calculus of variations. wikipedia articles are usually too sophisticated to understand on a straight cold reading

Answer 28

i mean without context

Answer 29

ok I'll see

Answer 30

i apologize for my comments earlier. i thought you were asking when does a function have an inverse

Answer 31

@perl , No worry, it's alright