Question

How do you find the inverse of `y= x^2-2x+1` and is it a function?

Answer 1

Inverse function of `y=x^2-2x+1` is `y=sqrtx+1`

Explanation:

`y=x^2-2x+1=(x-1)^2`

`x-1=sqrty`

`x=sqrty+1`

To find the inverse function, `f^-1(x)`, we replace the `x` with `y`. What we've now found is `x=f(y)`, but we want to find `f^-1(x)`. In order to do so, we simply switch `x` with `y`:

`f^-1(x) = sqrtx + 1`