The problem of finding onto and one one can be done as follow :
a) The graph of x2 - 2x + 3 is an upward parabola and hence not one one as there will be innumerable points which will be having same 'y' value for different 'x' value..Precisely about the axis of the parabola which is given by : x = 1 , an x coordinate and its mirror image about x = 1 will have same 'y' coordinate.
Hence the function is not one - one(injective).
b) To find whether it is onto or not , we find the range of the function :
y = x2 - 2x + 3
==> y = x2 - 2x + 1 + 2
= (x - 1)2 + 2
Now (x - 1)2 >= 0 always
Thus ymin = 0 + 2 = 2
So range of the given function : [ 2 , ∞ )
But given co-domain = set of integers denoted by Z..
Hence range becomes the proper subset of co domain in this case and hence the function is not onto(surjective) as for surjectivity , the condition is :
Range(function) = Co-Domain
Hence D) is the right answer..