Answer
Not one-to-one.
Work Step by Step
We are given:
$g(x)=2-2x+x^{2}$
We factor by completing the square:
$2-2x+x^{2}$
$x^2-2x+2$
$(x^{2}-2x+1)+1$
$(x-1)^{2}+1$
This function is not one-to-one because it fails the horizontal line test (it is a shifted parabola, which is an even function.) We can show that this function has the same $y$ value for two $x$ values:
$g(0)=2-2*0+0^2=2$
$g(2)=2-2*2+2^2=2-4+4=2$
Thus the function is not one-to-one.
