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

In summary, the conversation discusses finding the inverse of the function f(x) = -3x^2 + 6x + 2. The answer is +/- sqrt([2-x/3] + 1) + 1, which can be obtained by solving for x using the quadratic formula or completing the square. The textbook answer is the same as the given answer, but the domain must be restricted in order to get the inverse. The conversation also touches on the differences between the two inverse solutions and the process of finding the textbook answer.
  • #1
preet
98
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.
 
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  • #2
use complete square...
 
  • #3
I get +/- sqrt(x-5/-3) +1
 
  • #4
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.
 
  • #5
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...
 
  • #6
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?
 
  • #7
you mean with "x" as in
[tex] y=-3(x-1)^{2}+5 [/tex]

Now solve for "x"...

Daniel.
 
  • #8
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.
 
  • #9
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
 

1. What is the first step in finding the inverse of -3x^2+6x+2?

The first step in finding the inverse of a function is to switch the positions of the variables x and y. This will create a new equation in the form of y = f(x).

2. What is the next step after switching the positions of x and y in -3x^2+6x+2?

After switching the positions of x and y, solve for y. This will give you the inverse function in the form of y = f(x).

3. Can you solve for y in the equation -3x^2+6x+2?

Yes, you can solve for y by using the quadratic formula or by factoring the equation. Once you have solved for y, you will have the inverse function in the form of y = f(x).

4. What is the domain and range of the inverse function of -3x^2+6x+2?

The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function. In this case, the domain and range of the inverse function will be all real numbers.

5. How do you verify that the found inverse function is correct?

To verify that the inverse function is correct, you can use the composition method. Plug in the inverse function into the original function and vice versa. If the resulting equations simplify to x, then you have found the correct inverse function.

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