- #1

ZeroPivot

- 55

- 0

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter ZeroPivot
- Start date

- #1

ZeroPivot

- 55

- 0

- #2

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 970

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

ZeroPivot

- 55

- 0

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.

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

- #4

Office_Shredder

Staff Emeritus

Science Advisor

Gold Member

2021 Award

- 5,220

- 1,175

[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

- 36,324

- 8,286

"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

- 43,021

- 970

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

- #7

Mark44

Mentor

- 36,324

- 8,286

"Inversible" is not a word - the one you want is invertible.

Possibly because the adjectives invertible and reversible come from the verbs to invert and to reverse, respectively.

Share:

- Replies
- 2

- Views
- 314

- Last Post

- Replies
- 2

- Views
- 203

- Last Post

- Replies
- 13

- Views
- 260

- Last Post

- Replies
- 16

- Views
- 744

- Last Post

- Replies
- 2

- Views
- 609

- Last Post

- Replies
- 2

- Views
- 676

- Last Post

- Replies
- 1

- Views
- 198

- Replies
- 2

- Views
- 493

- Last Post

- Replies
- 7

- Views
- 482

- Last Post

- Replies
- 9

- Views
- 704