Answer
It is not a one-to-one function
Work Step by Step
$f(x) = 2 -2x + x^2$
One to one if f(p) = f(q)
$f(p) = 2 - 2p + p^2$
$f(q) = 2 - 2q + q^2$
$ 2 -2p + p^2 = 2 - 2q + q^2$
$p^2 - q^2 - 2(p-q) = 0$
$(p-q)(p+q) - 2(p-q) = 0$
$(p-q)(p+q - 2) = 0$
So p = q and p = 2-q
Thus it is not a one-to-one function
