Thread: Points for an inverse relation.

I promise, this is the last question for a while.

I need 4 points for the inverse of this relation:

y = 2|x|-1

I dunno how to make absolute values using the MATH button.

But yeah, I did think about substituting 2, 1, -1, -2 in for X, but is that the same as inverse?

Originally Posted by mankvill

I promise, this is the last question for a while.

I need 4 points for the inverse of this relation:

y = 2|x|-1

I dunno how to make absolute values using the MATH button.

But yeah, I did think about substituting 2, 1, -1, -2 in for X, but is that the same as inverse?

By inverse relation do you mean inverse function?

If so then consider that



and

Originally Posted by Mathstud28

By inverse relation do you mean inverse function?
If so then consider that

you can not consider it inverse function as y=2|x|-1 is not one to one function which is a neccesary condition for a function to have inverse.

I think you really mean inverse relation
y=2|x|-1
y=2x-1 if x>0
x=(y+1)/2>0
x=(y+1)/2 y>-1 or
y=(x+1)/2 x>-1(only interchanged x and y because generally x is taken to represent independent variable)
so we obtained the inverse relation (or inverse function if we particularly talk about y=2x-1 if x>0 as overall y=2|x|-1 do not have an inverse function) similarly same procedure can be followed for y=-2x-1 if x<0. (every function is a relation but every relation is not a function and every function may not have an inverse function)

so here is the easy Method
you said you need 4 points of inverse relation. So put any arbitrary value of x in the equation then interchange the range and domain for example let x=2 then y=2|x|-1
=2|2|-1=3 so the obtained point for relation is (2,3) now interchanging range and domain, point for inverse relation will be (3,2). Remember (3,-2) will also be an element of inverse relation
(3,2) and (3,-2) are not valid points points for a function.

Originally Posted by nikhil

you can not consider it inverse function as y=2|x|-1 is not one to one function which is a neccesary condition for a function to have inverse.

They never specified, but based on other problems by this poster, I assumed they accidentally omited a domain on which the function is to be considered, which based on the domain would make the function injective.

EDIT: But thank you very much, I shouldn't assume.