Inverse of a function

  • #1
anthonych414
86
0

Homework Statement



I need to find the inverse of y=x+√(x^2-1)

Homework Equations





The Attempt at a Solution



I know it's undefined from x=-1 and x=1 so there must be two different inverse functions on two different intervals. I don't know how to find them though.
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
43,010
969
You find the inverse pretty much the way you find any inverse:
Given [itex]y= x+ \sqrt{x^2- 1}[/itex], solve for x. Since there is a square root, we will want to square, and, in order not to get another square root in the "cross term" we want it by itself: [itex]y- x= \sqrt{x^2- 1}[/itex]. Now square that and solve for x.

Note the while x cannot be between -1 and 1, y can go to 0.
 
  • #3
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,576
1,167

Homework Statement



I need to find the inverse of y=x+√(x^2-1)

Homework Equations



The Attempt at a Solution



I know it's undefined from x=-1 and x=1 so there must be two different inverse functions on two different intervals. I don't know how to find them though.
Let's call the function you are given, f, so that
[itex]f(x)=x+\sqrt{x^2-1}\ .[/itex]​

Following HallsofIvy's suggestion you will find:
[itex]x=g(y)\ .[/itex]​
For the function, g, to be the inverse of function, f, it must also be true that g is the inverse of f. However, the domain of g will need to be restricted (to the range of f) so that g is a 1 to 1 function.
 

Suggested for: Inverse of a function

  • Last Post
Replies
6
Views
706
  • Last Post
Replies
2
Views
982
  • Last Post
Replies
0
Views
973
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
8
Views
12K
  • Last Post
Replies
12
Views
983
Replies
4
Views
2K
  • Last Post
Replies
4
Views
13K
Top