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Question -

Let A = {−1, 0, 1} and f = {(x, x2): x  A}. Showthat f : A → A is neither one-one nor onto.



Answer -

Given A = {−1, 0,1} and f = {(x, x2): x  A}

Also given that, f(x) = x2

Now we have to provethat given function neither one-one or nor onto.

Injectivity:

Let x = 1

Therefore f(1) = 12=1and

f(-1)=(-1)2=1

1 and -1 have thesame images.

So, f is not one-one.

Surjectivity:

Co-domain of f = {-1, 0, 1}

f(1) = 12 =1,

f(-1) = (-1)2 = 1 and

f(0) = 0

Rangeof f  = {0, 1}

So, both are not same.

Hence, f is not onto

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