Find Inverse of -3x^2+6x+2 - TiA

Click For Summary

Homework Help Overview

The discussion revolves around finding the inverse of the quadratic function f(x) = -3x^2 + 6x + 2. Participants are exploring the implications of the function's properties on the existence of an inverse.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss various methods to find the inverse, including switching variables, completing the square, and using the quadratic formula. There are questions about the validity of the inverse due to the nature of the quadratic function.

Discussion Status

The conversation is ongoing, with participants sharing their attempts and questioning the assumptions about the function's invertibility. Some have noted the need to restrict the domain to obtain valid inverses, while others express confusion about the differences in their results compared to the textbook answer.

Contextual Notes

There is a recognition that the function does not have a traditional inverse without domain restrictions, as it is a quadratic function. The vertex of the parabola is mentioned as a critical point in determining the nature of the inverses.

preet
Messages
96
Reaction score
0
How do I find the inverse of the following function: f(x)= -3x^2 + 6x + 2
The answer is +/- sqrt( [2-x/3] +1 ) + 1

I have no idea how to get that answer. I tried switching x and y and solving for x but I can't get the answer. TiA.
 
Physics news on Phys.org
use complete square...
 
I get +/- sqrt(x-5/-3) +1
 
Can u solve a quadratic equation?

If so,then solve for [itex]x=x(y)[/itex] from the equation
[tex]y=-3x^{2}+6x+2[/tex]

Or you can complete the square...Correctly...

Daniel.
 
walk me through it... completing the square, I get -3(y-1)^2 + 5 ... and I wrote the inverse of that. I just want to know what I'm doing wrong...
 
if your answer read like +/- sqrt((x-5)/-3) +1, then your answer is completely same as the textbook answer... why do you need help?
 
you mean with "x" as in
[tex]y=-3(x-1)^{2}+5[/tex]

Now solve for "x"...

Daniel.
 
Strictly speaking, f(x)= -3x2+ 6x+ 2 doesn't have an inverse!

Set y= -3x2+ 6x+ 2 and then use the quadratic formula to solve the quadratic equation -3x2+ 6x+ (2- y)= 0. You will see a + or - in the formula. In order to get an inverse, we need to restrict the domain. Since the vertex of the parabola is (1, 0.5), if x< 1 we get one inverse (with the -) and if x> 1 we get the other.
 
Yeah, I drew the graph... that's why I put +/- ... + is one inverse, - is the other

... I see that it's the same now... I don't get why they're different though... I mean I could tack on +1 -1 etc. How was the textbook answer found... (just out of curiosity)?

TiA
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
1K
Replies
8
Views
2K
Replies
2
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 15 ·
Replies
15
Views
3K
  • · Replies 15 ·
Replies
15
Views
3K
Replies
24
Views
4K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K