[Discrete Maths] : Functions

Question

Comments

@rahul it is x1+x2 = 2
(x1-x2)(x1+x2) = 2(x1-x2)

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I think it is coming as x1+x2=2

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Yes.I overlooked it.Thanks.

Answer 1

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   y_min  =    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..

Comments

Since domain has only positive value and 0.So there will be only two points where for different x ,y is same. i.e. 0 and 2. It will have upward parabola but since negative number not in domain ,so it will have half parabola on positive side,i dont know what we call it:p