Thread: Inverse of Quadratic Function?

Hi - I guess this is easy but I am having trouble solving it. I am supposed to find the inverse of the quadratic function

y = x^2 - 2x +1

Thanks in advance for any help, I am not sure if I can just factor it? The answer is supposed to be y = 1 +- srqrt X

Originally Posted by fumanchu

Hi - I guess this is easy but I am having trouble solving it. I am supposed to find the inverse of the quadratic function

y = x^2 - 2x +1

Thanks in advance for any help, I am not sure if I can just factor it? The answer is supposed to be y = 1 +- srqrt X

You start by substituting x with y:

x = y^2 - 2y + 1. Now we want to express y in terms of x. So, factor the polynomial:

x = (y-1)^2.

Therefore, y-1 = +-SQRT(x), so y = 1 +- SQRT(x).

Thanks sorry I didn't get it at first.

Do you know of a place that explains why the x ends up as + or - sqrt(x) when you take the square root. I understand that is the answer but I don't really get why. Sorry again.

Originally Posted by fumanchu

Do you know of a place that explains why the x ends up as + or - sqrt(x) when you take the square root. I understand that is the answer but I don't really get why. Sorry again.

this is so because whwn u mutiply a neg. no. by itself(-a*-a) the result will come positive.
and if u multiply a positive no. with itself(a*a) the result will be positive.
so it cant be made out if the sqrt was originally posit. or neg.. so to be on the safer side we take both +&-.

Originally Posted by fumanchu

Do you know of a place that explains why the x ends up as + or - sqrt(x) when you take the square root.

You get the "plus-minus" from the Quadratic Formula or, if you prefer, from completing the square. (But that's the hard way!)

Wait, that can't be the inverse function. When you have the plus-minus sign, you have a one-to-many relation, so it is not a function! The exercise must give the original's function domain and codomain if you are expected to find its inverse.

But the exercise, as originally posted, did not ask for an inverse function; it asked only for "the inverse". The "plus-minus" relation fulfills that requirement.

Well, I suppose this is just semantics and is really irrelevant, but the OP did say "find the inverse of the quadratic function" and the inverse of a function must also be a function. So it must be asking the inverse function.

Originally Posted by Referos

...the inverse of a function must also be a function.

No; only some functions are "invertible"; only some functions have inverses which are also themselves functions. Usually, the inverse is just a "relation".