Question

How to find the inverse of y= 3x^2-12x+1

Answer 1

I am tying to find the inverse of this function

Answer 2

:S ohhhh umm errr

Answer 3

put y in for each x

Answer 4

at least i believe thats how you do it

Answer 5

I know that but to find the inverse you need to factor it... How do you do that???

Answer 6

First complete the square for x

y= 3x^2-12x+1

y-1= 3x^2-12x

y-1 = 3(x^2-4x)

y-1 = 3(x^2-4x+4-4) ... see note below

y-1 = 3((x^2-4x+4)-4)

y-1 = 3((x-2)^2-4)

y-1 = 3(x-2)^2-3(4)

y-1 = 3(x-2)^2-12

y = 3(x-2)^2-12+1

y = 3(x-2)^2-11


Note: I took half of the x coefficient -4 to get -4/2 = -2. Then I squared that result to get (-2)^2 = 4. You then add and subtract 4 to x^2 - 4x to complete the square to get x^2 - 4x + 4 - 4. The trinomial x^2 - 4x + 4 will factor to (x-2)^2 which is a perfect square. So this is how x^2 - 4x turns into (x-2)^2 - 4

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So

y= 3x^2-12x+1

is equivalent to

y = 3(x-2)^2-11

Answer 7

Now you swap x and y, then solve for y

y = 3(x-2)^2-11

x = 3(y-2)^2-11

x+11 = 3(y-2)^2

3(y-2)^2 = x+11

(y-2)^2 = (x+11)/3

y-2 = +-sqrt( (x+11)/3 )

y = 2+-sqrt( (x+11)/3 )


The sign on the square root will depend on what the initial domain of the original function. So if x > 2, then you'll be focusing on the upper half which will mean you use the "plus" (instead of the "minus)


So again, if x > 2, then the inverse is


y = 2 + sqrt( (x+11)/3 )

Answer 8

Thanks alot Sir, your explaation made sense to me and I finally got it