f(x)=x²-3x+2

The best way is first to see if you can prove it isn't one-to-one.
If you can you're done.  If you can't, only then try to prove that it
is.

Here's how to try to prove it isn't one-to-one:

1.  Choose an arbitrary number in the domain of f(x) to substitute
    for x.  Say x=0.

2.  Substitute it for x

    f(0)=(0)²-3(0)+2
    f(0)=2

3.  Set the original expression for f(x) equal to the result of step 2.
    and solve for x

    x²-3x+2=2
      x²-3x=0
      x(x-3)=0
   x=0;  x-3=0
           x=3

4.  If you get another value for x in the domain of f(x), then you
    have shown that it is not one-to-one.

    We have shown that f(x) is not one-to-one because both 0 and 3
    are in the domain of f(x) and f(0) = f(3) = 2.
     
    Essentially we have shown that f(x) contains two distinct points 
    with the same y-coordinate namely (0,2) and (3,2), so it isn't
    one-to-one.

Edwin