Question -
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