Q. 11

# Let f: R →<

f: R R be defined as f(x) = x4.

Let x, y ϵ R such that f(x) = f(y)

x4 = y4

x = y

Therefore, f(x1) = f(x2) which does not implies x1 = x2.

For instance, f(1) = f(-1) = 1

Therefore, f is not one-one.

Now, an element 2 in co-domain R.

We can see that there does not exist any x in domain R such that

f(x) = 2

Therefore, f is not onto.

Therefore, function f is neither one-one nor onto.

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