How do I find the Inverse function for
x^2-8x+8 ?
p.s This is for Algebra 2
I want help not just the answer please.

Question

zepdrix · Answer

So we have a function:$$\Large f(x)=x^2-8x+8$$We'll replace our function notation with y, since it's a little easier to work with in these types of problems.$$\Large y=x^2-8x+8$$To find the inverse, we have all of our x's and y's trade places,$$\Large x=y^2-8y+8$$And from here to find the inverse function, we solve for our new y.
Hmm so it's going to be a tad tricky since we have different degrees of y.
We'll need to complete the square on the y's.

To complete the square, we take half of the b term and square it.
In this problem we have $\large b=-8$.
Half of that is $\large -4$, then squared is $\large 16$.

So our constant term needs to be $\large 16$.
So we'll need another $\large 8$.
Let's add $\large 8$ to each side.$$\Large x+8=y^2-8y+16$$

zepdrix · Answer

Completing the square on the right simplifies it down to,$$\Large x+8=(y-4)^2$$To further solve for y we would take the square root and do some math stuff.