- #1

- 54

- 0

## Main Question or Discussion Point

can a function thats not inversable be inversible in certain interwalls. is it ok to say its inversable in this specific intervall or cant the function ever be called inversible?

- Thread starter ZeroPivot
- Start date

- #1

- 54

- 0

can a function thats not inversable be inversible in certain interwalls. is it ok to say its inversable in this specific intervall or cant the function ever be called inversible?

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 955

For example, [itex]f(x)= x^2[/itex]is not "invertible" because it is neither "one to one" nor "onto". However, if we restrict the domain to the "non-negative real numbers" then its inverse is [itex]\sqrt{x}[/itex]. If we restrict the domain to the "non-positive real numbers" then its inverse is [itex]-\sqrt{x}[/itex].

However, the

- #3

- 54

- 0

can i say function y=x^2 is inversible for x E [0 ,4] ?

For example, [itex]f(x)= x^2[/itex]is not "invertible" because it is neither "one to one" nor "onto". However, if we restrict the domain to the "non-negative real numbers" then its inverse is [itex]\sqrt{x}[/itex]. If we restrict the domain to the "non-positive real numbers" then its inverse is [itex]-\sqrt{x}[/itex].

However, thedomainof a function is as much a part of its definition as the "formula". That is, "[itex]f(x)= x^2[/itex], for x any real number", "[itex]g(x)=x^2[/itex], for x any non-negative real number", and [itex]h(x)= x^2[/itex], for x any non-negative real number" are three different functions. The first does not have an inverse, the last two do.

- #4

Office_Shredder

Staff Emeritus

Science Advisor

Gold Member

- 3,750

- 99

[tex] f: [0,4]\to [0,16],\ x\mapsto x^2 [/tex]

is an invertible function because of the domain that has been specified (also it needs to have the right codomain, or it won't be an onto function, but that's more of a technicality that is washed away by restricting the codomain to whatever the range is)

- #5

Mark44

Mentor

- 33,505

- 5,191

"Inversible" is not a word - the one you want is invertible.can i say function y=x^2 is inversible for x E [0 ,4] ?

- #6

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 955

So why is "reversible" a word and not "revertible"?

- #7

Mark44

Mentor

- 33,505

- 5,191

Possibly because the adjectives invertible and reversible come from the verbs to invert and to reverse, respectively."Inversible" is not a word - the one you want is invertible.

- Replies
- 5

- Views
- 896

- Last Post

- Replies
- 3

- Views
- 3K

- Last Post

- Replies
- 1

- Views
- 625

- Last Post

- Replies
- 14

- Views
- 4K

- Last Post

- Replies
- 7

- Views
- 4K

- Last Post

- Replies
- 5

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 581

- Last Post

- Replies
- 12

- Views
- 3K

- Last Post

- Replies
- 3

- Views
- 523

- Last Post

- Replies
- 3

- Views
- 2K